LEARNING MATHS is a series of nine Mathematics textbooks for Classes Introductory to 8. Conforming to the National Curriculum Framework, the series aims to develop thinking and reasoning skills among students by connecting the mathematics curriculum with real-life situations. To make the books user-friendly, mathematical concepts are introduced and explained thoroughly before moving on to essential drill and practice. Key Features of the Primary Series The revised edition of Learning Maths for primary classes has been developed to create a passion for the subject among the learners. The key features are: Graded content with an interactive learning pattern for maximum involvement of children Practice Section for additional drilling includes Revision Exercise, Speedy Maths, Tricky Maths, Mental Maths, MCQs, Math Lab Activity, and much more to meet the curriculum requirement Value Based Questions and Problem Solving Assessment introduce a variety of real-life situations, and guide students to tackle the problems by strategizing Higher Order Thinking Skill (HOTS) questions include challenges that trigger analytical reasoning Worksheets at the end of each chapter present fun-filled posers enhance interest in mathematics The books are supplemented by enriched Teacher s manual Animated audio-visual CDs to integrate concept building. They support book content through visuals, animations and interactive exercises. We also offer Web support for teachers at www.frankedu.com
Problem solving Assessment (develop problem solving skills) Value based Questions (real life applications) Mental Maths (strategies for fast calculation) Tricky Maths (build thinking skills) Speedy Maths (sharpen mathematical skills) Interactive Learning Pattern Math Lab (build concepts through activities) Worksheet (interactive form of practice)
CHAPTER Number and Numeration Lesson Plan OBJECTIVES The students should know about (i) The smallest and the greatest -digit and 6-digit numbers (ii) System of numeration (iii) Expanded and short form of the numbers (iv) Place value system of 7-digit, 8-digit and 9-digit numbers (v) International place value system (vi) Comparison of numbers (vii) Ascending and descending order of numbers Prerequisite Knowledge: The students should have the basic knowledge of 3-digit, 4-digit, -digit and 6-digit numbers as they have studied in their previous classes. Teaching Aids: Writing board, marker, chalks, charts, duster, geometrical box, smart-board/ projector and the pointer. Method of Teaching: The following topics of this chapter will be taught in the class by giving simple examples. (i) Revision of -digit and 6-digit numbers and their expanded form. (ii) System of numeration (a) Indian place value chart Period Lakhs Thousands Ones Place value TL L TTh Th H T O Numbers 00000 0000 000 00 0 (b) International place value chart Period Thousands Ones Place value HTh TTh Th H T O Numbers 00000 0000 000 00 0 (iii) 7-digit numbers: (a) Smallest 7-digit number = 000000 (b) Greatest 7-digit number = 9999999 (iv) 8-digit numbers: (a) Smallest 8-digit number = 0000000 (b) Greatest 8-digit number = 99999999 (v) 9-digit numbers: (a) Smallest 9-digit number = 00000000 (b) Greatest 9-digit number = 999999999 (vi) Expanded form: 94703 = 9 0000000 + 000000 + 4 00000 + 7 0000 + 000 + 3 0 + Recapitulation: The whole chapter will be revised in the class by giving some extra questions and the problems will be solved accordingly. TH Learning Maths Price : `92.00 3
(A) From Textbook 4 Home Assignments (i) Exercise. Solve Q. No. to 0 all parts (ii) Exercise.3 Solve Q. No. to all parts (iii) Exercise. Solve Q. No. to 6 all parts (B) Extra Questions (i) Write the expanded form of 830030. (ii) Write the following numbers in ascending order. 83689, 88369, 83698, 89836 Exercise. Textbook Solutions.-0. Refer answers at the end of the book.. TTh Th H T O Smallest no. 3 0 4 6 8 (0 will not come at the ten thousands place, otherwise Biggest no. 8 6 4 3 0 it will become a 4-digit number) 2. Smallest number Greatest number L TTh Th H T O L TTh Th H T O a. 3 0 0 0 9 9 9 9 3 0 b. 2 2 7 7 7 7 2 2 c. 2 4 7 8 8 8 7 4 2 3. a. 270 b. 3000 c. 600 Exercise.2.-2. Refer answers at the end of the book. 3. a. Greatest 6-digit number = 999999 Greatest -digit number = 99999 Total 6-digit numbers = Greatest 6-digit number Greatest -digit number = 999999 99999 = 900000 b-c. Similar working as above. 4. Refer answers at the end of the book.. a.,77,89;,77,892;,77,893; ;,77,899 b. 2,8,00,20; 2,8,00,206; 2,8,00,207; ; 2,8,00,224 c. 44,44,44,44; 44,44,44,446; 44,44,44,447; ; 44,44,44,43 Exercise.3. 6. Refer answers at the end of the book. 7. Indian Place Value Chart Period Crores Lakhs Thousands Ones Place TC C TL L TTh Th H T O a. 4322342 4 3 2 2 3 4 2 b. 904030300 9 0 4 0 3 0 3 0 0 c. 67009 6 7 0 0 9 d. 874023 8 7 4 0 2 3 e. 770423 7 7 0 4 2 3 f. 39930046 3 9 9 3 0 0 4 6 TH Learning Maths
International Place Value Chart Period Billions Millions Thousands Ones Place HB TB B HM TM M HTTh TTh Th H T O a. 4322342 4 3 2 2 3 4 2 b. 904030300 9 0 4 0 3 0 3 0 0 c. 67009 6 7 0 0 9 d. 874023 8 7 4 0 2 3 e. 770423 7 7 0 4 2 3 f. 39930046 3 9 9 3 0 0 4 6 8. Refer answers at the end of the book. Exercise.4 4. Refer answers at the end of the book.. a. 70000 + 400 = 70400 b. 7000000 + 60000 + 80 = 7060080 c. 0 + 3000 = 3000 d. 700000 + 0 = 700000 e. 0000000 + 600000 = 0600000 f. 90000000 + 400000 = 90400000 6. a. 400000 8000 = 392000 b. 00000 8000 = 492000 c. 400000000 40000000 = 360000000 d. 7000000 8000 = 6992000 e. 7000000 0 = 7000000 f. 900000000 9000000 = 89000000 Exercise.. 4. Refer answers at the end of the book.. a. 3, 2, 7, 8, 4, 6,, To write the greatest 7-digit number, we select 7 digits starting from the greatest. They are 3, 2, 7, 8, 4, 6 and. Now place them in such a way that the greatest digit occupies the greatest place, i.e., 876432 is the greatest seven-digit number. Similarly, to form smallest seven-digit number, we place smaller 7 digits in such a way that the smallest come at the highest place, i.e., 23467 is the smallest seven-digit number. Similarly, for eight digits, the greatest numeral is 876432 and the smallest numeral is 234678. b. 0, 2, 4,, 3, 6, 8, 9 Seven greater digits are 9, 8, 6, 4, 3, 2 and. Hence greatest seven-digit number = 986432 and Seven smaller digits are 0,, 2, 3, 4, 6 and 8. Hence, smallest seven-digit number = 023468 Greatest eight-digit number using 0, 2, 4,, 3, 6, 8, 9 = 9864320 Smallest eight-digit number = 0234689. Remember that 0 cannot be placed at crore s place as it will become a seven-digit number. 6. 8. Refer answers at the end of the book. 9. Smallest 8-digit number = 0000000 Greatest number using digits 3, 8, 6,,, 2, 0 is 86320. TH Learning Maths
Difference = 0000000 86320 346790 Smallest number using digits 3, 8, 6,,, 2, 0 is 02368. Difference = 0000000 02368 8976432 0. Greatest 8-digit number = 99999999 Greatest 7-digit number = 9999999 Difference = 90000000 Greatest 8-digit number = 99999999 Smallest 7-digit number = 000000 Difference = 98999999 Exercise.6. 8. Refer answers at the end of the book. Test Your Skills Multiple Choice Questions.. Refer answers at the end of the book. Apply Your Skills Problem Solving Assessment. Refer answers at the end of the book. 2. As 7089 7098, 8079 8097. So, 9078 9087. 3. TL L TTh Th H T O 8 7 6 4 2 0 2 8 7 6 4 0 4 8 7 6 2 0 6 8 7 4 2 0 7 8 6 4 2 0 8 7 6 4 2 0 4., 0,, 2, 3, 4,, 6, 7, 8, 9, 2, 3, 4,, 6, 7, 8, 9, 00 = 2 times. a. Rewrite the numeral with commas after every three digits starting from the right.,624,608 b. 7,00,000 = 700, 000 c. 4 hours (as rounding off to the nearest hour, ignore less than half an hour). 6 TH Learning Maths
Value Based Questions. All cars when rounded off will be near to `4,00,000. Since the budget is `4,00,000, it should be better to go for car D as it may have some better features than car B. Value: Friendship 2. Refer answers at the end of the book. HOTS. Any five numbers out of 20000, 2000,..., 349999 can be written. (Answers may vary) 2. Refer answers at the end of the book. 3. TL L TTh Th H T O 0 0 0 0 4 6 0 0 0 0 6 4 4 0 0 0 0 6 4 0 0 0 0 6 6 0 0 0 0 4 Mental Maths. Refer answers at the end of the book. 2. 308008 = 3 0000000 + 000000 + 8 0000 + 0 + 8 3. 7,80, 4 8,67 < 7,80, 8 4,67 4. Yes, since :0 is more than :30, it can be rounded off to 6:00 am.. 2,6,308 0 = 263080 ~ 2600000; No. 000046 < 000064 < 400006 < 400006 < 600004 2 CHAPTER Roman Numerals Lesson Plan OBJECTIVES The students should know about (i) Roman numerals and Hindu-Arabic numerals (ii) Rules of conversion (iii) Comparison of numerals Prerequisite Knowledge: The students should have the basic knowledge of the Roman numerals as they have studied in their previous classes. Teaching Aids: Writing board, marker, chalk, chart, duster, geometrical box, smart-board/ projector and the pointer. Method of Teaching: The following topics of this chapter will be taught in the class with simple examples. (i) Roman Numerals: I V X L C D M Hindu-Arabic Numerals: 0 0 00 00 000 TH Learning Maths 7
(ii) Rules of Conversion: (a) Example: Convert 29 to Roman numerals. 29 = 2000 + 900 + 0 + = MMCMLV (b) Example: Convert MCMXXXI to Hindu-Arabic numerals. Here, M is 000, CM is 900, XXX is 30 and I is. \ MCMXXXI = 000 + 900 + 30 + = 93 Note: To write the numerals equal to or greater than 4000, viniculum is used. E.g.: IV = 4000, X = 0000, etc. (iii) Comparison of Roman Numerals Example: Compare XCIII and CIX. Here XCIII = 93 and CIX = 09 XCIII < CIX Recapitulation: The whole chapter will be revised in the class by taking some simple and suitable examples and the problem of the students, if any, will be solved immediately. (A) From Textbook (i) Exercise 2. Solve Q. No. to 7 all parts Home Assignments (ii) Test Your Skills Solve Q. No. to all parts (B) Extra Questions (i) Convert 832 to Roman numerals. (ii) Convert MMCXXIV to Hindu-Arabic numerals. (iii) Compare LXIX and LXXV. Exercise 2.. 6. Refer answers at the end of the book. Textbook Solutions 7. a. XXXVIII = 38 b. LXXXVI = 86 XXV = 2 XI = Sum = 63 = LXIII Sum = 97 = XCVII c. CX = 0 d. XXVII = 27 XC = 90 XXIII = 23 Difference = 20 = XX Difference = 4 = IV e. CC VI = 200 6 f. LXI XVII = 6 7 = 200 = MCC = 037 = MXXXVII g. CCL XXV = 20 2 h. MMM L = 3000 0 = 0 = X = 60 = LX Test Your Skills Multiple Choice Questions.. Refer answers at the end of the book. 8 TH Learning Maths
Apply Your Skills Problem Solving Assessment. Rafiq LXV Dolly CLI Satinder XIV, XVI a. Largest number = CLI c. Satinder b. Smallest number = XIV d. Dolly Value Based Questions. Refer answers at the end of the book. 2. I, V, X, IV, IX, VI, XI, XV, XIV, XVI Total sections = 0, maximum number of saplings = 6 Minimum number of saplings =. Value: Care for environment HOTS Refer answers at the end of the book. Mental Maths. 3, 9, 6, 67, 7, 73, 79, 83, 89, 97 LIII, LIX, LXI, LXVII, LXXI, LXXIII, LXXIX, LXXXIII, LXXXIX, XCVII 2. 9 4 + 7 0 + 29 = 76 + 0 + 29 = 00 = C 3. th August 947 = XV/VIII/MCMXLVII 4. 23, 477, 774, 389 477 < 774 < 389 < 23 CDLXXVII < DCCLXXIV < MCCLXXXIV < MMCXXXV. Successor of 80 = 8 = MDCCCLI 3 CHAPTER Addition and Subtraction Lesson Plan OBJECTIVES The students should know about (i) Addition and subtraction and their properties (ii) Addition without carryover (iii) Addition with carryover (iv) Word problems and their formation (v) Estimations of addition and subtraction Prerequisite Knowledge: The students should have the basic knowledge of addition and subtraction of smaller numbers as they have done in their previous classes. TH Learning Maths 9
Teaching Aids: Writing board, marker, chalks, charts, duster, geometrical box, smart-board/ projector and the pointer. Method of Teaching: The following topics and subtopics of this chapter will be taught in the class with some extra suitable examples. (i) Properties of Addition and Subtraction (a) When 0 is added to a number, the sum is the number itself. 0 + 438 = 438 + 0 = 438 (b) When is added to a number, we get the next number (successor) and if is subtracted from it, we get the previous number (predecessor). 438 + = 439 438 = 437 (c) When a number is subtracted from itself, we get 0. 468 468 = 0 (d) Commutative property: If the order of two numbers to be added is changed, the sum remains the same. 823 + 0 = 0 + 823 = 873 (e) Associative property: The sum of any three or more numbers remains the same, if their grouping is changed. 34 + (870 + 28) = (34 + 870) + 28 = 482 (ii) Addition of 7-digit numbers without carryover TL L TTh Th H T O 2 2 3 2 6 + 3 6 2 7 8 8 7 7 6 (iii) Addition of 7-digit numbers with carryover TL L TTh Th H T O 2 8 3 6 8 + 2 9 8 7 8 2 8 2 4 2 3 0 (iv) Word problems and Estimation of addition to be taught in the class with suitable examples. Recapitulation: The whole chapter will be revised in the class with extra questions and the problems of the students will be solved accordingly. (A) From Textbook Home Assignments (i) Exercise 3.2 Solve Q. No. and 2 all parts. (ii) Exercise 3.4 Solve Q. No. to all parts. (iii) Exercise 3.6 Solve Q. No. and 2 all parts. 0 TH Learning Maths
(B) Extra Questions (i) Add: 384 + 62 + 302 using associative property (ii) Subtract: 8632 from 9768 Exercise 3. Textbook Solutions. 3. Refer answers at the end of the book. 4. a. Distance from city B to C = 623 km Distance from city A to B = 3282 km Difference = 24049 km Thus, the train covers 24049 km more distance to travel from city B to C. d. No of men = 2342 No. of women = 432692 No. of children = + 22342 774 \ Total population of the city is 774. b & c. Similar working as above. Exercise 3.2. Refer answers at the end of the book. 2. a. 060408 + 22739 2287799 2287799 Twenty-two lakh eighty-seven thousand seven hundred ninety-nine c. 2842 74287 + 4499087 26626 26626 Fifty-two lakh sixty-six thousand two hundred sixteen Exercise 3.3. 2. Refer answers at the end of the book. 3. a. 243674 + 848 802422 b. 327644 + 720466 07380 07380 One crore seven lakh thirty-one thousand eight hundred ten. d. 924477 39042 + 23469 79878 79878 Seventy-one lakh ninety-eight thousand one hundred seventy-eight b. Similar working as in (a). 802422 Eight crore two lakh fourteen thousand two hundred fifty-two TH Learning Maths
c. 876366 236009 + 07783 207740 Exercise 3.4 207740 Two crore ten lakh seventyseven thousand four hundred ten d. 8708777 0788 + 9900866 4867. a. Production of toys in 20 202 = 36983 Production of toys in 202 203 = + 867842 Total production of toys in 20 203 = 3937673 b. Production of toys in 202 203 = 867842 Production of toys in 203 204 = Total production of toys in 202 204 = 4867 Fourteen crore eighty-one lakh sixty-seven thousand one hundred fifty-five + 967839 28246237 c. Total production of toys in 20 20 = 36983+ 867842 + 967839 + 23698743 = 7348 2. Cost of house = `6324 Cost of office = + `83628 Total = `399432 Total money spent by Mohan Lal is `399432. 3. Books sold in st week = 4262273 Books sold in 2nd week = + 83240 Total books sold = 2794283 Total books sold at the end of two weeks is 2794283. 4. Number of copies sold in January = 74623 Number of copies sold in February = 774098 Number of copies sold in March = + 278492 Total copies sold = 430944 Total copies sold in three months is 430944.. Money allocated in 203 = `387498 Money allocated in 204 = Money allocated in 20 = Total money allocated = `334928 + `3742627 `0930936 Total money allocated for planting trees is `0930936. 6 8. Refer answers at the end of the book. Exercise 3.. a. Actual sum Estimated sum 444 400 24 200 + 879 + 900 37 00 Difference between the actual sum and estimated sum is 37 00 = 37. 2 TH Learning Maths
b. Actual sum Estimated sum 269 300 792 800 + 73 + 700 2792 2800 Difference between the actual sum and estimated sum is 2800 2792 = 8. c. Actual sum Estimated sum 342 879 + 89 36 300 900 + 900 300 Difference between the actual sum and estimated sum is 36 300 = 6. d. Actual sum Estimated sum 343 486 + 7284 83 300 00 + 7300 800 Difference between the actual sum and estimated sum is 83 800 = 3. 2. a. Actual sum Estimated sum 486 349 + 7426 3640 000 000 + 7000 3000 Difference between the actual sum and estimated sum is 3640 3000 = 640. b. Actual sum Estimated sum 8462 49 + 2942 289 8000 000 + 3000 2000 Difference between the actual sum and estimated sum is 289 2000 = 89. c. Actual sum Estimated sum 462 8029 + 4862 2743 000 8000 + 000 28000 Difference between the actual sum and estimated sum is 28000 2743 = 47. d. Actual sum Estimated sum 342 6882 + 3449 8282 3000 7000 + 3000 83000 Difference between the actual sum and estimated sum is 83000 8282 = 48. TH Learning Maths 3
4 3. a. Actual sum Estimated sum 23948 20000 2736 0000 + 438 + 0000 306 20000 Difference between the actual sum and estimated sum is 306 20000 = 06. b. Actual sum Estimated sum 63048 7420 + 8092 60 60000 0000 + 90000 60000 Difference between the actual sum and estimated sum is 60000 60 = 4440. c. Actual sum Estimated sum 33333 30000 48 0000 + 3624 + 40000 24389 20000 Difference between the actual sum and estimated sum is 24389 20000 = 4389. d. Actual sum Estimated sum 74926 70000 23440 20000 + 326609 + 330000 2497 20000 Difference between the actual sum and estimated sum is 2497 20000 = 497. 4. a. Actual cost Estimated cost (rounding off to nearest tens) `378 `380 `49 `0 `32 `30 + `772 + `770 `30 `300 Difference between actual cost and estimated cost is `(30 300) = `. Estimation is accurate. b. Actual cost Estimated cost (rounding off to nearest hundreds) `378 `49 `32 + `772 `30 `400 `00 `400 + `800 `300 Exercise 3.6 Difference between estimated cost and actual cost is `(300 30) = `49. Estimation is accurate. 2. Refer answers at the end of the book. 3. a. One of the number = 97262987 Difference = Other number = Other number is 996844. 8806643 996844 TH Learning Maths
b. Sum = 7843278 One number = 84328 9888960 9888960 should be added to 84328 to get 7843278. c. Greatest number of 8 digits = 99999999 Number = 634748 36424 36424 should be added to 634748 to get greatest 8-digit number. d. Money earned = `36287 Money spent = `3267898 Money saved = `2094289 He saved `2094289. e. Production after 2 years = 863267 Production initially = 346247 328920 Increase in the production was 328920 bottles. f. Greatest number = 98740 Smallest number = Difference = 04789 882962 Difference between greatest and smallest numbers using the digits 8,, 7, 0,, 4 and 9 = 882962 4. Do it yourself. Exercise 3.7. 4. Refer answers at the end of the book. Exercise 3.8. First find the sum of 2678232 and 3378470. 2678232 + 3378470 9462933 Now subtract 9462933 from 79836260. 79836260 9462933 20373327 2. First find the sum of 3622 and 268324. 3622 + 268324 402084 Now find the sum of 432624 and 6728. 432624 + 6728 9993782 Now subtract 402084 from 9993782. 9993782 402084 972937 TH Learning Maths
3. First find the sum of 7483267 and 2874032. 7483267 + 2874032 7747299 Now find the sum of 43874280 and 3264876. 43874280 + 3264876 47396 4. First find the sum of 672672 and 382426. 672672 + 382426 9494098 Now subtract 9494098 from 0000000. 0000000 9494098 0902 6. First add the number of students who voted for winner and who voted for loser. 9447932 + 7949268 7397200 Now subtract this sum from the total number of student votes. 7849600 7397200 42400 42400 students did not vote in the election. Now subtract 47396 from 7747299. 7747299 47396 303843 Thus, the sum of 7483267 and 2874032 is greater than the sum of 43874280 and 3264876 by 303843.. First find the sum of the children less than 0 years old and then find the number of people in the age group of 0 70 years. 273269 + 237862 4890 Now subtract 4890 from 834678. 834678 4890 282788 There are 282788 people whose age is more than 70 years. 7. First add the amount allocated in the first year and second year. st year 2nd year Total = `20844000 + `82400 `32426400 Now subtract this from the total annual allocation. `3784000 `32426400 `387600 The remaining amount to be allocated in the third year is `387600. 8. To find the number of magazine sold in July, subtract 40000 from 2739298. 2739298 40000 789298 So, 789298 magazines were sold in July. To find the number of magazines sold in August, add 724000 to 789298. 789298 + 724000 2473298 In the month of August, 2473298 magazines were sold. 6 TH Learning Maths
9. Refer answers at the end of the book. 0. Do it yourself. Mental Maths. Refer answers at the end of the book. Test Your Skills Multiple Choice Questions. Refer answers at the end of the book. Apply Your Skills Problem Solving Assessment. Number = (3806 + 26442) (3806 26442) = 64490 740 = 2880 2. 84 was added to 7384 instead of 48. Therefore, answer would be greater by 84 48 = 36. 3. a. 260 km + 40 km = 270 km b. 800 km + 080 km = 2880 km c. 490 km + 800 km + 40 km = 4740 km d. 800 km + 080 km + 20 km + 260 km = 6290 km 4. Quantity of grains left in the godown = 273680 (74260 + 42800) = 46620 quintals Value Based Questions. Number of books left = 7340 734 = 60, Value: Social responsibility 2. Area donated for dispensary = 394200 m 2 2430 m 2 = 36980 m 2, Value: Responsible citizen HOTS. Each of the three friends contributed `0. So their total contribution was `0 3 = `30 Amount of bill for 3 tea = `2 Hence, the amount waiter returned = `30 `2 = ` Now, each friend picked `, and `2 was given as tip to the waiter. Therefore, total payment = `2 + `2 = `27 And final expenses beared by the three friends = `(0 ) 3 = `27. Thus, total payment = total expenses, there was no missing of money. 2. Total no. of hens, goats and camels = 0 + 4 + 8 = 03 (heads) Total no. of legs of these animals = 0 2 + 4 4 + 8 4 = 00 + 80 + 32 = 32 Let no. of human keepers = So, no. of their heads = and their feet = 2 Total no. of feet is 224 more than the no. of heads. That means, 32 + 2 = (03 + ) + 224 Or, 32 + 2 = 327 + Or, = 327 32 = Thus, there are human keepers in the caravan. TH Learning Maths 7
4 CHAPTER Multiplication Lesson Plan OBJECTIVES The students should know about (i) Properties of multiplication (ii) Word problems based on multiplication (iii) Estimation of multiplication Prerequisite Knowledge: The students should have the basic knowledge of the multiplication of smaller numbers as they have done in their previous classes. Teaching Aids: Writing board, marker, chalks, chart, duster, geometrical box, smart-board/ projector and the pointer. Method of Teaching: The following topics of this chapter will be taught in the class by taking some extra questions. (i) Properties of multiplication (a) When a number is multiplied by 0, it becomes 0. (b) When a number is multiplied by, it remains the same. (c) Commutative property of multiplication: If order of multiplication of two numbers is changed, the resulting number will be same. 2 3 = 3 2 = 6 (d) Associative property of multiplication: If grouping of the multiplication of three numbers is changed, the resulting number will be same. 2 (3 ) = (2 3) = 2340 (ii) Word Problems: The cost of one book is `20, what will be the cost of 2 such books? Cost of book = `20 Cost of 2 such books = `20 2 = `620 Recapitulation: The whole chapter will be revised in the class by taking some simple examples and the problems of the students will be solved immediately. Home Assignments (A) From Textbook (i) Exercise 4. Solve Q. No. and 2 all parts. (ii) Exercise 4.3 Solve Q. No. to 3 all parts. (iii) Exercise 4.4 Solve Q. No. to. (iv) Exercise 4. Solve Q. No., 2, 3 all parts. (B) Extra Questions (i) Multiply 36 and 0 and verify commutative property of multiplication. (ii) Simplify: 36 080 0 23 (iii) Simplify: 8623 00 8 TH Learning Maths
Exercise 4.. a. 62 7 39347 Thirty-nine thousand three hundred fortyseven e. 44 33 6632 6632 8292 One lakh eightytwo thousand nine hundred fifty-two b. 862 9 7762 Textbook Solutions Seventy-seven thousand six hundred twenty-five f. 876 42 730 3060 36830 Three lakh sixtyeight thousand one hundred thirty c. 678 63 7034 34068 3774 Three lakh fiftyseven thousand seven hundred fourteen g. 6789 76 6789 40734 4723 66429 Fifty-one lakh sixtysix thousand four hundred twenty-nine d. 624 32 208 8762 20028 Two lakh one hundred twentyeight h. 7878 820 760 63024 649960 Sixty-four lakh fiftynine thousand nine hundred sixty 2. a. Cost of toy car = `462 Cost of 7 toy cars = `462 7 = `32347 b. Cost of book = `46 Cost of 624 books = `46 624 624 46 37284 2486 28844 c. Cost of bicycle = `62 Cost of 322 bicycles = `62 322 62 322 324 324 4686 Thus, cost of 624 books is `28844. 02964 Thus, cost of 322 bicycles is `02964. d. To find the bill paid by Mr. Mohan add answers obtained in (i), (ii) and (iii). i. Cost of dress = `36 Cost of 8 dresses = `36 8 = `4288 ii. Cost of book = `326 Cost of 63 books = `326 63 = `2038 326 63 978 96 2038 Total bill = `4288 `2038 + `926 `44082 iii. Cost of pizza = `232 Cost of 83 pizzas = `232 83 = `926 232 83 696 86 926 He paid `44082 in total. TH Learning Maths 9
e. Cost of one chair = `486 Cost of 764 chairs = 764 944 896 +0402 3304 Cost of 764 chairs is `3304. 3. Refer answers at the end of the book. Exercise 4.2. Refer answers at the end of the book. Exercise 4.3. a. 837 69 623 + 042 266633 2. a. 26732 62 3464 603920 + 3366000 023384 One crore fifty lakh twenty-three thousand three hundred eighty-four b. 26 333330 + 00 444430 b. 8394 8394 49720 + 839400 26769 One crore twentysix lakh seventy-five thousand six hundred ninety-five c. 602 8 30060 + 4809680 028 c. 7003 409 3027 000000 + 22802 2334227 Two crore thirty-three lakh fourteen thousand two hundred twentyseven 3. Refer answers at the end of the book. d. 38462 8 3083696 + 384620 693836 d. 24002 246 2402 060080 + 0800400 62484492 Six crore twentyfour lakh eighty-four thousand four hundred ninety-two e. 470896 8 470896 + 3767680 384276 e. 400634 323 20902 802680 + 2090200 29404782 Twelve crore ninety-four lakh four thousand seven hundred eighty-two f. 764897 2 29794 + 3824480 39774644 f. 6003 86 363020 + 48402800 203300 Five crore twenty lakh thirty-three thousand ten Exercise 4.4. Product of 324 and 74 = 324 74 = 240796 324 74 306 + 227780 240796 Greatest number formed by the digits 4, 7,, 3, 6, 8 is 87643. Now, 87643 240796 63747 2. Number of soap cakes in a carton = 40 8 40 Number of cartons = 8 0000 To find the number of soap cakes in 8 cartons, multiply 8 40. 7920 + 634000 There are 7320 soap cakes in the godown. 7320 20 TH Learning Maths
3. Smallest three-digit number using, 0, 7 is 07. 99999 Greatest five-digit number = 99999 07 Product of 07 99999 = 0699493. 699993 000000 + 4999900 0699493 4. Number of toys made in one day = 326406 Number of toys made in 24 days = 326406 24 7833744 toys are produced in 24 days. 326406 24 30624 + 62820 7833744. Cost of 7 bags of urea = `36 7 = `62300 Cost of 24 bags of phosphorus = `4 24 = `8880 Total amount spent by Surjeet singh = `(62300 + 8880) = `0 6. Cost of shirt = `6 Cost of 3624 shirts = `3624 6 = `6344 3624 6 2744 8200 + 362400 6344 Cost of trouser = `867 Cost of 467 trousers = `867 467 = `39989 467 867 3969 274020 + 363600 39989 Total money earned by the shopkeeper = `6344 + `39989 = `424933. 7. Weight of bag = 0 kg Number of bags of wheat a truck can carry = 883 Weight a truck can carry = 0 883 kg = 3240 kg Weight carried by 6 trucks = 3240 6 kg = 860920 kg 8. Number of bags of rice = 24 Weight of bag rice = 9 kg Total weight of 24 bags of rice = 24 9 kg = 20330 kg TH Learning Maths 2
Cost of kg rice = `38 Cost of 20330 kg rice = 38 20330 = `77240 9. One day earning = `97 One month or 26 days earning = `97 26 = `24882 One year (or 2 months) earning = `24882 2 = `29884 0. Do it yourself. Exercise 4. -4. Refer answers at the end of the book.. a. Sugar in a bag = 96 kg = 00 kg (approx) Weight of 32 bags of sugar = 30 00 = 3000 kg b. Rate of ball = `8 = `20 (approx) Rate of 243 balls = `240 20 = `4800 c. Cost of kg of wheat = `24 = `20 (approx) Cost of 374 kg of wheat = `370 20 = `7400 Exercise 4.6. a. 0 + 6 + 0 + = 8 + 2 + + 8 + 0 + 2 = 4 2 + + 2 + 6 + + 6 = 2 2 3 4 3 0 6 0 8 0 6 2 6 2 2 2 0 2 8 2 2 4 7 + 2 + 0 + + 2 + = 7 8 + 2 + = \ 247 343 = 8427 b. 4 2 0 + = 0 0 8 0 4 3 + 8 + = 2 3 4 2 0 6 + 2 + 4 + 0 + 0 + = 8 2 0 6 0 8 2 + 6 + 2 + 0 + + 4 + = 6 2 2 0 0 2 2 + 0 + 2 + 0 + 0 + 6 + 2 = 2 3 4 0 2 4 + 3 + + + 8 = 2 2 0 + + 0 = \ 2846 42 = 28622 2 8 4 6 22 TH Learning Maths
c. 0 0 + 2 + 0 = 2 0 + 4 + = 0 + 8 + = 9 0 + 9 + + 0 + 0 + 0 + 2 = 2 0 + 6 + + 8 + 8 + 0 + 0 + = 2 4 2 9 0 2 0 4 8 0 0 0 0 0 0 0 0 0 9 0 6 0 7 0 0 8 2 4 0 0 8 4 6 3 7 + + 2 + + + = 7 3 4 + 6 + 4 = 4 \ 200967 29 = 2924743 2 0 0 9 6 7 e. 2 4 0 0 2 2 0 0 0 + + + = 7 0 3 2 6 2 0 4 6 0 + 6 + + 0 + 2 + 2 = 0 4 3 8 6 0 2 8 0 + 8 + + 2 + 3 + + 2 + 2 = 2 3 0 4 3 9 8 6 9 9 + + 6 + 4 + 0 + 2 + 0 + 2 = 2 4 6 8 + 4 + 0 + 3 + 4 + = 2 0 \ 689 24 = 734006 + 3 + 2 = 0 d and f. Similar working as above. Test Your Skills Multiple Choice Questions.. Refer answers at the end of the book. Puzzles. 0 0 0 + 0000 + 000 020 a =, b = 0 2. Steps Activity Outcome. Think of a number 0 2. Add 2 0 + 2 = 7 3. Double it 7 2 = 0 4. Add 40 0 + 40 = 90. Divide by 2 90 2 = 9 6. Take away the number you started with. 9 0 = 4 Mental Maths. 240 99 = 240 (00 ) = 24000 240 = 2420 2. (2000 + 80 + ) 03 = 206000 + 8240 + 03 = 24343 3. Associative property TH Learning Maths 23
4. 400 4000 = 600000, True. No. of lines in the notebook = 2 27 = 337 Apply Your Skills Problem Solving Assessment. Income on st day = `00 Income on 2nd day = 2 00 = `200 Income on 3rd day = 2 200 = `400 or 2 2 00 = `400 Income on 4th day = 2 2 2 00 = `800 Income on 0th day = 2 2 2 2 2 2 2 2 2 00 = `,200 2. No. of biscuits = 60 0 = 3000 No. of friends = 6 No. of biscuits 6 friends have in a day = 6 0 = 60 Number of days = 3000 = 0 60 3. Number of apples in a box = 48 Number of apples in 240 boxes = 240 48 or Number of apples in a truck = 240 48 Number of apples in 2 trucks = 2 240 48 = 440000 4. Number of books in one room = 72 84 = 6048 Number of books in another room = 2 43 = 37 As 6048 > 37, so st room has more books. Value Based Questions. Capacity of the auditorium = 90 60 = 400 seats Number of seats reserved for physically handicapped = 0 60 = 600 seats Number of seats reserved for EWS category = 60 = 300 seats; Value: Social responsibility. 2. Number of icecreams in packets = 0 = 0 Cost of packets = `0 = `70; Value: Concern for poor. HOTS. Height climbed by the mountaineer in a day = 473 metres Height climbed by the mountaineer in 6 days = 473 6 = 768 metres Height left to climb = (8848 768) m = 280 m 2. Number of pencils = 8 27 = 90 Number of erasers = 72 24 = 8928 Number of notebooks = 60 4 = 2700 24 TH Learning Maths
CHAPTER Division Lesson Plan OBJECTIVES The students should know about (i) Division and its properties (ii) Relation between dividend, divisor, quotient and the remainder (iii) Word problems based on division process (iv) Estimation of division (v) Unitary method Prerequisite Knowledge: The students should have the basic knowledge of division of smaller numbers as they have done in their previous classes. Teaching Aids: Writing board, marker, chalks, charts, duster, geometrical box, smart-board/ projector and the pointer. Method of Teaching: The following topics and sub-topics of this chapter will be taught in the class. (i) Properties of division (a) If a number is divided by itself, the result is always. (b) If a number is divided by, the result will always be the same number. (c) Number divided by 0 will not be defined. (d) A number is said to be completely divisible by other number, if the remainder is 0. (ii) Division of big numbers by 2-digit numbers. Example: Divide 830 by. 6 7 ) 8 3 0 ( 7 8 7 00 90 0 0 0 (iii) Word problems: A school needs `00 for a new project, how much money each of the students have to pay? Contributions of students = `00 \ Contribution of student = `00 = `300 Recapitulation: The whole chapter will be revised in the class with simple examples. If the students have any problem, that will be solved immediately. TH Learning Maths 2
Home Assignments (A) From Textbook (i) Exercise.2 Solve Q. No., 2, 3 all parts (ii) Exercise.3 Solve Q. No. and 2 all parts (iii) Exercise.4 Solve Q. No. to 3 all parts (iv) Exercise. Solve Q. No. to 0 (B) Extra Questions (i) Divide 837 by 23 and find the quotient and the remainder. (ii) Divide 746789 by 32 and verify your answer. (iii) What will be the cost of a bicycle if a shopkeeper sold 27 bicycles for `47987? Exercise. Textbook Solutions. a. 430 b. 44 0 c. 72 64 430 86 40 30 30 6 44 9 04 40 64 72 4 66 96 Q = 86 Q = 9, R = 40 Q = 4, R = 96 d. 206 9 e. 607 8 f. 8928 93 9 206 224 8 2 8 36 36 8 607 7 67 40 40 Q = 224 Q = 7 Q = 96 g. 3780 24 h. 206 329 24 3780 4 24 240 06 224 329 206 6 974 42 Q = 4, R = 224 Q = 6, R = 42 2. a. 2 objects = dozen 392 objects = 392 2 = 326 There are 326 dozens in 392 objects. b. Number of trees = 326 Number of gardens = 37 Number of trees in each garden = 326 37 = 88 Number of trees in each garden is 88. 8 8 3 7 3 2 6 2 9 6 2 9 6 2 9 6 ) ( 93 8928 96 837 8 8 3 2 6 2 3 9 2 3 6 3 2 4 7 2 7 2 ) ( 26 TH Learning Maths
c. Number to be multiplied = 4032 72 = 6 6 should be multiplied by 72 to get 4032. d. Cost of book = `04 Number of books that can be bought for `8424 = 8424 04 = 8 8 books can be bought for `8424. e. Cost of 4 kg rice = `236 Cost of kg rice = `236 4 = `34 Cost of kg rice is `34. Exercise.2. 2. Refer answers at the end of the book. 3. Do it yourself. Exercise.3. a. 67892 74 74 67892 97 666 29 74 2 8 34 Q = 97, R = 34 b. 4386 86 86 4386 632 6 278 28 206 72 34 Q = 632, R = 34 c. 28672 28672 622 2 37 306 02 32 02 30 Q = 622, R = 30 3 4 4 2 3 6 4 6 2 6 6 6 6 ) ( 8 0 4 8 4 2 4 8 3 2 0 4 0 4 ) ( 6 7 2 4 0 3 2 3 6 0 4 3 2 4 3 2 ) ( Verification Dividend = Quotient Divisor + Remainder = 97 74 + 34 = 6788 + 34 = 67892 Verification Dividend = Quotient Divisor + Remainder = 632 86 + 34 = 432 + 34 = 4386 Verification Dividend = Quotient Divisor + Remainder = 622 + 30 = 286722 + 30 = 28672 TH Learning Maths 27
d. 48432 68 68 48432 674 408 04 476 283 272 2 68 44 Q = 674, R = 44 Verification Dividend = Quotient Divisor + Remainder = 674 68 + 44 = 48388 + 44 = 48432 e. 726908 8 8 726908 232 8 46 6 309 290 90 74 68 6 2 Q = 232, R = 2 f. 2947349 36 36 2947349 8870 288 67 36 33 288 24 22 29 29 29 Q = 8870, R = 29 Verification Dividend = Quotient Divisor + Remainder = 232 8 + 2 = 72686 + 2 = 726908 Verification Dividend = Quotient Divisor + Remainder = 8870 36 + 29 = 2947320 + 29 = 2947349 g. 07602 84 84 07602 2804 84 23 68 676 672 402 336 66 Q = 2804, R = 66 Verification Dividend = Quotient Divisor + Remainder = 2804 84 + 66 = 0736 + 66 = 07602 28 TH Learning Maths
h. 6483692 9 9 6483692 098930 9 83 3 26 472 49 3 82 77 00 Q = 098930, R = Verification Dividend = Quotient Divisor + Remainder = 098930 9 + = 64836870 + = 6483692 2. a. Dividend = Divisor Quotient + Remainder = 47 32 + 3 = 087 + 3 = 00 Dividend = 00 b. Quotient = (Dividend Remainder) Divisor = (637428 2) 24 = 63746 24 = 269 Quotient = 269 c. Dividend = Quotient Divisor + Remainder = 2643 38 + 28 = 2000434 + 28 = 2000462 Dividend = 2000462 d. Dividend = 6783 Divisor = 62 62 6783 9 8 98 62 363 30 3 Q = 9, R = 3 e. Dividend = 7896 Divisor = 26 26 7896 30369 78 96 78 8 6 2 234 2 Q = 30369, R = 2 TH Learning Maths 29
f. Dividend = 87649 Divisor = 69 69 87649 2703 69 86 38 48 483 24 207 349 34 4 Q = 2703, R = 4 Exercise.4. Refer answers at the end of the book. 2. a. 86732 37 37 86732 233 742 23 3 402 3 289 Q = 233, R = 289 b. 9673 632 632 9673 3 632 33 360 93 896 7 Q = 3, R = 7 c. 87643 423 423 87643 2072 846 304 296 0933 846 87 Q = 2072, R = 87 Verification Dividend = Quotient Divisor + Remainder = 233 37 + 289 = 86443 + 289 = 86732 Verification Dividend = Quotient Divisor + Remainder = 3 632 + 7 = 96696 + 7 = 9673 Verification Dividend = Quotient Divisor + Remainder = 2072 423 + 87 = 87646 + 87 = 87643 30 TH Learning Maths
d. 4433 67 67 4433 82 400 443 30 933 67 28 Q = 82, R = 28 e. 028672 22 22 028672 99 22 208 2268 2406 2268 387 260 272 260 2 Q = 99, R = 2 f. 467620 467620 8092 420 4762 463 270 030 240 Q = 8092, R = 240 g. 230240 48 48 230240 0 48 822 740 82 740 84 740 740 740 Q = 0, R = Verification Dividend = Divisor Quotient + Remainder = 67 82 + 28 = 47 + 28 = 4433 Verification Dividend = Divisor Quotient + Remainder = 22 99 + 2 = 028660 + 2 = 028672 Verification Dividend = Divisor Quotient + Remainder = 8092 + 240 = 467380 + 240 = 467620 Verification Dividend = Divisor Quotient + Remainder = 48 0 + = 2302400 + = 230240 TH Learning Maths 3
h. 360720 227 227 360720 686 227 290 3 7 362 9 86 392 362 300 227 73 Q = 686, R = 73 3. a. Dividend = Divisor Quotient + Remainder = 32 234 + 46 = 3964 + 46 = 39660 Dividend = 39660 42 63247 322 b. 42 382 27 074 80 2247 22 22 80 37 Q = 322, R = 37 c. Dividend = Divisor Quotient + Remainder Divisor = (Dividend Remainder) Quotient = (482397 893) 008 = 4822704 008 = 963 d. Remainder = Dividend Divisor Quotient = 26789 23 22943 = 26789 2660 Remainder = 84 e. Dividend = Quotient Divisor + Remainder = 884 83 + 30 = 493223 + 30 = 493276 Yes, the given sum is correct. Dividend = Divisor Quotient + Remainder = 227 686 + 73 = 3607447 + 73 = 360720 32 TH Learning Maths
Exercise.. Divisor = 43 Quotient = 643 Remainder = 46 Dividend = Divisor Quotient + Remainder = 43 643 + 46 = 24470 + 46 = 2447 The number was 2447. 2. Apples in one carton = 63 Cartons required to pack 82427 apples = 82427 63 63 82427 32400 689 3 26 222 222 7 32400 cartons are required to pack 82427 apples and 7 apples will be left. 3. To find the number that must be subtracted from 86039 so that the given number 86039, is exactly divisible by 328, we need to find the remainder when 86039 is divided by 328. 328 86039 67 640 2203 968 239 2296 63 63 must be subtracted from 86039 to make it exactly divisible by 328. 4. Greatest 6-digit number = 999999 Greatest 3-digit number using 7, 8 and 9 = 987 Now divide 999999 by 987 and subtract the remainder, so obtained from 999999 to get the largest six digit number divisible by 987. 987 999999 03 987 299 987 329 296 68 999999 68 = 99983 99983 is the largest six-digit number exactly divisible by 987. TH Learning Maths 33
34. 342789 + 826439 = 689334 27 689334 4483 028 409 28 243 028 23 206 974 77 203 Sum of the given number is not exactly divisible by 27 and remainder is 203. 6. Number of students = 86 Total amount collected = 342400 paise = `3424 (divide 342400 by 00) Amount donated by each student = `3424 86 = `4 Each student donated `4. 7. Selling price of 27 bicycles = `47987 Selling price of bicycle = `47987 27 = `74 8. Total students = 67 + 73 = 40 Total mess fees paid = `7080 Mess fees paid by one student = `7080 40 = `222 Each student paid `222. 9. Cost of 364 microchips = `27984 Cost of microchip = `27984 364 = `346 Cost of 36 defective microchips = `346 36 = `47006 Cost of remaining microchips = `27984 `47006 = `787968 0. Greatest 7-digit number = 9999999 Greatest number using 3, 7, 4 = 743 743 9999999 348 743 269 2229 3409 2972 4379 37 6649 944 70 TH Learning Maths
Divisor = 743 Quotient = 348 Dividend = 9999999 Remainder = 70 Dividend = Divisor Quotient + Remainder = 743 348 + 70. Total consumption of vegetables in the month of August to November = 47963324 Total days in August + September + October + November = 3 + 30 + 3 + 30 = 22 Consumption of vegetables in a day = 47963324 22 = 39342 kg 39342 kg of vegetables is consumed per day. 2. Do it yourself. Exercise.6. a. 49 is rounded to 0 b. 84 is rounded to 80 4 is rounded to 0 63 is rounded to 60 0 0 = 3 80 60 = 3 c. 396 is rounded to 400 d. 79 is rounded to 720 44 is rounded to 40 84 is rounded to 80 400 40 = 0 720 80 = 9 e. 2974 is rounded to 2970 f. 2877 is rounded to 2880 3 is rounded to 30 77 is rounded to 80 2970 30 = 99 2880 80 = 36 g. 4863 is rounded to 4860 h. 849 is rounded to 80 63 is rounded to 60 49 is rounded to 0 4860 60 = 8 80 0 = 7 Exercise.7. Weight of bag = 0 = 30 kg 2. No. of pens in box = 20 = 0 No. of pens in 40 boxes = 0 40 = 2000 3. Time taken to fill full water tank = 2 2 = 4 hours Time taken to fill water tanks by water pipe = 4 = 20 hours 4. No. of words Nimit typed in second = 6 8 = 2 No. of words Nimit typed in 2 minutes = 2 60 2 = 240. Weight of gold piece = 620 = 08 g No. of gold pieces = 760 08 = 70 6. Length of wire = 90 6 = m a. Length of 0 wires = 0 = 0 m b. No. of wires for 30 m = 30 = 2 TH Learning Maths 3
7. Distance covered by athlete in minute = 480 = 60 metres 8 Distance covered by athlete in 20 minutes = 60 20 = 200 metres So, athlete can cover 200 m or km 200 m in 20 minutes. 8. Same working as above. Test Your Skills Multiple Choice Questions.. Refer answers at the end of the book. 6 0 3 4 2 6 2 ) 9 7 7 4 0 4 9 7 2 4 4 8 6 6 8 0 6 4 8 3 2 4 3 2 4 Apply Your Skills Problem Solving Assessment. Number of pieces = 22600 90 = 2 90 22600 2 80 460 40 00 90 0 36 2. Amount donated by a family = `977404 62 = `60342 3. Number of stands = 20000 22 = 88 22 20000 88 800 2000 800 200 Number of people left out = 200 4. To find the least number, divide 72800 by 83 and then subtract the remainder from 72800. 83 72800 877 664 640 8 90 8 9 Number exactly divisible by 83 = 72800 9 = 7279 7279 83 = 877 Thus, 9 is the required number.. To find the least number, we first divide 4626 by 28. 79 28 = 4682 < 4626 So, we take the quotient as 80. 80 28 = 46440 Now, subtract 46440 4626 = 224 Thus, least number that should be added to be 224. 28 4626 79 28 204 806 236 2322 34 TH Learning Maths
Value Based Questions. Money 782 people donated = `3406392 So, money donated by person = 3406392 = `436 782 Money 987 people will donate = `436 987 = `42,99,372; Value: Care for others 2. Number of months = 4,00,000 2000 = 400 2 = 200 Number of months and years = 200 months 2 = 6 years 8 months; Value: Social work 3. Number of minutes = 4400 60 = 240 Number of hours = 240 60 = 4; Value: Sincerity HOTS. We will take 2 at ones and thousands places as the number lies between 2000 and 3000. Hundreds digit = 2 2 = 3 Tens digit is a prime number less than 3, so it is 2. Th H T O 2 3 2 2 Also, 2322 is divisible by 29. 2. Water in 2 tanks = 2 3000 = 7000 litres No. of drums = 2 = 37. Mental Maths. Refer answers at the end of the book. 6 CHAPTER Multiples and Factors Lesson Plan OBJECTIVES The students should know about (i) Factors and common factors (ii) Multiples and common multiples (iii) Prime and composite numbers (iv) Even and odd numbers (v) Divisibility rules (vi) LCM and HCF (vii) Relationship between LCM and HCF Prerequisite Knowledge: The students should have the basic knowledge of factors and multiples as they have done in their previous classes. TH Learning Maths 37
Teaching Aids: Writing board, marker, chalks, charts, duster, geometrical box, smart-board/ projector and pointer. Method of Teaching: The following topics and sub-topics included in this chapter will be taught in the class with some simple and suitable examples. (i) Factors and Common factors Factors of 0 =, 2,, 0 Factors of =, 3,, Common factor = (ii) Prime and Composite numbers (a) Prime numbers: Numbers which are not divisible by any number except or itself. Example, 2, 3,, 7,, 3, ( is not prime) (b) Twin Prime Numbers: A pair of prime numbers which are differ by 2. (2, 3), (3, ), (, 7), (, 3), (7, 9), etc. (iii) Composite Numbers: A number which has more than two factors. Example, 6 =, 2, 3, 6; 2 =, 2, 3, 4, 6, 2 (iv) Lowest Common Multiple (LCM) Example: Find the LCM of 2 and 8. Multiples of 2 = 2, 24, 36, 48, 60, 72,... Multiples of 8 = 8, 36, 4, 72, 90,... Common multiples = 36, 72,... \ LCM = 36 (v) Highest Common Factors Example: Find the HCF of 24 and 30. Factors of 24 =, 2, 3, 4, 6, 8, 2, 24 Factors of 30 =, 2, 3,, 6, 0,, 30 Common factors =, 2, 3 and 6 \ HCF = 6 Recapitulation: The whole chapter will be revised in the class by involving the students in group and the problem of the students will be solved immediately. Home Assignments (A) From Textbook (i) Exercise 6. Solve Q. No. to all parts. (ii) Exercise 6.3 Solve Q. No. to 8 all parts. (iii) Exercise 6.4 Solve Q. No. to 3 all parts. (B) Extra Questions (i) Find the LCM of 8, 2, 20 and 24. (ii) Find the HCF of 24 and 36. (iii) Write all the prime numbers less than 0. (iv) Write all the twin prime numbers between 0 and 60. 38 TH Learning Maths
Exercise 6.. Refer answers at the end of the book. 2. a. 9 36 4 36 0 Textbook Solutions b. 3 26 6 3 86 78 6 Since remainder is zero, Remainder is 6, so 3 is not a hence 9 is a factor of 36. factor of 26. c. 2 2 2 2 is a factor of 2. 3. a. 24 = 24, 2 2, 3 8, 4 6, 6 4 Factors of 24 are, 2, 3, 4, 6, 8, 2 and 24 c. 80 = 80, 2 40, 4 20, 6, 8 0 Factors of 80 are, 2, 4,, 8, 0, 6, 20, 40 and 80. e. 22 = 22, 3 7, 4,, 9 2 Factors of 22 are, 3,, 9,, 2, 4, 7 and 22. 4. a. Factors of 4 are, 2, 7, 4. Factors of 3 are,, 7, 3. Common factors of 4 and 3 are and 7. b. Factors of 27 are, 3, 9, 27 Factors of 36 are, 2, 3, 4, 6, 9, 2, 8, 36 Common factors of 27 and 36 are, 3 and 9. c. Factors of 48 are, 2, 3, 4, 6, 8, 2, 6, 24, 48 Factors of 32 are, 2, 4, 8, 6, 32 Common factor of 48 and 32 are, 2, 4, 8 and 6. d. Factors of 36 are, 2, 3, 4, 6, 9, 2, 8, 36 Factors of 4 are, 3,, 9,, 4 Common factors of 36 and 4 are, 3 and 9. e. Factors of 64 are, 2, 4, 8, 6, 32, 64 Factors of 96 are, 2, 3, 4, 6, 8, 6, 32, 48, 96 Common factors of 64 and 96 are, 2, 4, 8, 6 and 32. 8. Refer answers at the end of the book. Exercise 6.2 b. 36 = 36, 2 8, 3 2, 4 9, 6 6 Factors of 36 are, 2, 3, 4, 6, 9, 2, 8 and 36. d. 08 = 08, 2 4, 3 36, 4 27, 6 8, 9 2 Factors of 08 are, 2, 3, 4, 6, 9, 2, 8, 27, 36, 4 and 08.. a. 36 is a composite number as it has more than 2 factors, i.e.,, 2, 3, 4, 6, 9, 2, 8, 36 are its factors. TH Learning Maths 39
b. 37 is prime as it has only two factors and 37. c. 3 is prime as it has only two factors and 3. d. 9 is a prime as it has only two factors and 9. e. 8 is a composite as its has more than two factors, i.e.,, 3, 9, 27 and 8. 2 9. Refer answers at the end of the book. 0. a. and 33 Factors of are, 3,, Factors of 33 are, 3,, 33 Common factors of and 33 are and 3. and 33 are not co-prime as they have 3 as common factor other than. b. 24 and 29 Factors of 24 are, 2, 3, 4, 6, 8, 2 and 24 Factors of 29 are, 29 Common factors of 24 and 29 is only. Hence they are co-prime. c 34 and 7 Common factors of 34 are, 2, 7, 34 Common factors of 7 are, 3, 9, 7 Common factors of 34 and 7 is. Hence 34 and 7 are co-prime. d. 8 and 67 Factors of 8 are, 2, 3, 6, 9 and 8 Factors of 67 are, 67 Common factors of 8 and 67 is. Hence 8 and 67 are co-prime. e. 4 and 2 Factors of 4 are, 2, 7 and 4 Factors of 2 are, 2, 4, 3, 26, 2 Common factors of 4 and 2 is and 2. Hence they are not co-prime. Exercise 6.3 40. Refer answers at the end of the book. 2. a. 4623 and e. 887 unit digits are 3 and so they are not divisible by 2. b. 9000 c 438 d. 796 and f. 2004 has units digits as 0, 8, 6 and 4 so they all are divisible by 2. 3. a. 323 = 3 + + 2 + 3 = 9 b. 4826 = 4 + 8 + 2 + 6 = 20 c. 296 = + 2 + + 9 + 6 = 27 d. 7632 = 7 + 6 + 3 + 2 + = 9 e. 84463 = 8 + 4 + 4 + 6 + 3 = 2 Sum of digits of a. and c. is divisible by 3, hence 323 and 296 are divisible by 3. 4. a. 486 b. 2 c. 4920 d. 7773 e. 9636 f. 8862 The number formed by last two digits of b, c and e, i.e., 2, 20 and 36 are divisible by 4, hence b, c and e are divisible by 4. TH Learning Maths
. a. 92 b. 7732 c. 9008 d. 46246 e. 83224 Since 92, 008, 224 are divisible by 8, so the number 92, 9008 and 83224 are divisible by 8. 6. a. 6987 = 6 + 9 + 8 + 7 = 30 b. 8424 = 8 + 4 + 2 + 4 = 8 c. 940 = 9 + 4 + 0 + = 8 d. 0049 = + 0 + 0 + 4 + 9 = 8 e. 68978 = 6 + 8 + 9 + 7 + 8 = 38 Sum of digits of 8424, 940 and 0049 is divisible by 9, so 8424, 940 and 0049 are divisible by 9. 7. a. + + 9 + 2 + = 7 + A number greater than 7 divisible by 3 is 8, so 8 7 = should be there in the box as the smallest digit so that the number so formed is divisible by 3. b. 8 + + 2 + 2 = 2 + 2 is divisible by 3, so the smallest digit that can be filled in the blank is 0. c. 9 6; Sum of digits = + 9 + 6 + = 20 + The smallest number greater than 20 but divisible by 3 is 2, so 2 20 = should be at the blank space. d. 2 + 2 + + + = 3 + The smallest number greater than 3 and divisible by 3 is. So 3 = 2 should be the digit at the blank space. 8. a. 49 8 0 as 08 or 8 is divisible by 4. b. 340 2 as 2 is divisible by 4. c. 42 2 as 2 is divisible by 4. d. 3927 2 as 72 is divisible by 4. 9. a. 36 6 as 66 is divisible by 8. b. 3726 4 as 264 is divisible by 8. c. 637 4 0 as 704 is divisible by 8. d. 83 2 as 32 is divisible by 8. 0. a. 72 = + 7 + 2 + = 4 + A number greater than 4, divisible by 9 is 8, hence 8 4 = 4 is the digit to be fitted in the blank space. b. 47 8 = 4 + 7 + + 8 + = 24 + A number greater than 24 but divisible by 9 is 27, so 27 24 = 3 is the digit to be fitted in the blank space. c. 97 = + 9 + 7 + + = 22 + A number greater than 22, but divisible by 9 is 27, hence 27 22 = is the digit to be fitted in the blank space. d. 4 2 = 4 + + 2 + = 7 + A number greater than 7, but divisible by 9 is 9, hence 9 7 = 2. So 2 is to be fitted in the blank space. TH Learning Maths 4
Exercise 6.4. a. 24, 33 Factors of 24 =, 2, 3, 4, 6, 8, 2, 24 Factors of 33 =, 3,, 33 Common factors of 24 and 33 = and 3 \ HCF of 24 and 33 = 3 b. 36, 22 Factors of 36 =, 2, 3, 4, 6, 9, 2, 8, 36 Factors of 22 =, 2, 3, 4, 6, 7, 9, 2, 4, 8, 2, 28, 36, 42, 63, 84, 26, 22 Common factors of 36 and 22 =, 2, 3, 4, 9, 2, 8, 36 \ HCF = 36 c. e. Similar working as above. 2. a. 42, 84 2 42 3 2 7 7 2 84 2 42 3 2 7 7 7 7 42 = 2 3 84 = 2 3 2 \ HCF of (42, 84) = 2 3 7 = 42. c. 2, 90 2 2 90 4 3 9 3 3 2 = 90 = 2 3 3 \ HCF of (2, 90) = e. 8, 24, 32 2 8 3 9 3 3 2 24 2 2 2 6 3 3 2 32 2 6 2 8 2 4 2 2 8 = 2 3 3 24 = 2 2 2 3 32 = 2 2 2 2 2 \ HCF of (8, 24, 32) = 2 b. 36, 63 2 36 2 8 3 9 3 3 3 63 3 2 7 7 36 = 2 2 3 3 63 = 7 3 3 \ HCF of (36, 63) = 3 3 = 9. d. 2, 8, 27 2 2 2 6 3 3 2 8 3 9 3 3 3 27 3 9 3 3 2 = 2 2 3 8 = 2 3 3 27 = 3 3 3 \ HCF of (2, 8, 27) = 3 f. 22, 66, 2 2 22 2 66 3 33 2 22 = 2 66 = 2 3 2 = \ HCF of (22, 66, 2) = 42 TH Learning Maths
g. 2, 6, 9 2 6 3 3 9 9 9 2 = 6 = 3 9 = 9 \ HCF of 2, 6, 9 = i. 08, 36, 2 h. 64, 80, 20 2 64 2 32 2 6 2 8 2 4 2 2 2 80 2 40 2 20 2 0 2 20 2 60 2 30 3 64 = 2 2 2 2 2 2 80 = 2 2 2 2 20 = 2 2 2 3 \ HCF of (64, 80, 20) = 2 2 2 = 8 2 08 2 4 3 27 3 9 3 3 2 36 2 68 2 34 7 7 2 2 2 76 2 38 9 9 08 = 2 2 3 3 3 36 = 2 2 2 7 2 = 2 2 2 9 \ HCF of (08, 36, 2) = 2 2 = 4 3. a. 2, 28 2 28 2 24 4 2 3 2 HCF of (2, 28) = 4. c. 78, 20 78 20 2 6 4 78 4 24 4 2 48 6 24 4 24 HCF of (78, 20) = 6. b. 42, 330 42 330 7 294 36 42 36 6 36 6 36 HCF of (42, 330) = 6. d. 60, 420 and 924 60 420 7 420 60 924 60 324 300 24 60 2 48 2 24 2 24 HCF of (60, 420, 924) = 2. TH Learning Maths 43
44 e. 4, 770, 90 4 770 770 4 90 770 40 4 40 4 40 0 40 H.C.F. (4, 770, 90) = 4. Exercise 6.. a. 30, 7 Multiples of 30 = 30, 60, 90, 20, 0, 80 Multiples of 7 = 7, 0, 22 Common multiples of 30 and 7 = 0, 300,... \ LCM of (30, 7) = 0 c. 20, 2, 60 20, 2, 60 2 4,, 2 2 2,, 6,, 3 3,, 3,, LCM of (20, 2, 60) = 2 2 3 = 300 2. a. 28, 3 2 28 3 2 4 7 7 7 7 28 = 2 2 7 3 = 7 LCM = 2 2 7 = 40 LCM of (28, 3) = 40 f. 20, 420, 40 20 420 2 420 20 40 2 420 20 20 20 90 20 90 30 90 3 90 b. 4, 66 HCF of (20, 420, 40) = 30. 3 4, 66 2, 22 3,,,, LCM of (4, 66) = 3 2 3 = 990 d. 36, 63, 8 3 36, 63, 8 3 2, 2, 27 3 4, 7, 9 3 4, 7, 3 7 4, 7, 2 4,, 2 2,,,, LCM of (36, 63, 8) = 3 3 3 3 7 2 2 = 2268 b. 48, 72 2 48 2 72 2 24 2 36 2 2 2 8 2 6 3 9 3 3 3 3 48 = 2 2 2 2 3 72 = 2 2 2 3 3 LCM = 2 2 2 2 3 3 = 44 \ LCM of (48, 72) = 44 TH Learning Maths
c. 22, 66 2 22 2 66 3 33 22 = 2 66 = 2 3 \ LCM of (22, 66) = 2 3 = 66 e. 2, 80, 20 2 2 80 2 20 2 2 90 0 3 4 3 2 3 7 7 2 = 80 = 2 2 3 3 20 = 2 3 7 \ LCM of (2, 80, 20) = 3 3 2 2 7 = 300 3. a. 20, 3, 4 20, 3, 4 2 4, 7, 9 2 2, 7, 9 7, 7, 9 3,, 9 3,, 3,, \ LCM of (20, 3, 4) = 2 2 7 3 3 = 260 c. 27, 4, 60, 72, 96 3 27, 4, 60, 72, 96 3 9,, 20, 24, 32 3 3,, 20, 8, 32,, 20, 8, 32 2,, 4, 8, 32 2,, 2, 4, 6 2,,, 2, 8 2,,,, 4 2,,,, 2,,,, \ LCM of (27, 4, 60, 72, 96) = 3 3 3 2 2 2 2 2 = 4320 d. 36, 48, 96 2 36 2 48 2 96 2 8 2 24 2 48 3 9 2 2 2 24 3 3 2 6 2 2 3 3 2 6 3 3 36 = 2 2 3 3 48 = 2 2 3 2 2 96 = 2 2 3 2 2 2 \ LCM of (36, 48, 96) = 2 2 2 2 2 3 3 = 288 f. 98, 26, 360 2 98 2 26 2 360 3 99 2 08 2 80 3 33 2 4 2 90 3 27 3 4 3 9 3 3 3 98 = 2 3 3 26 = 2 2 2 3 3 3 360 = 2 2 2 3 3 \ LCM of (98, 26, 360) = 2 2 2 3 3 3 = 880 b. 0, 2, 6 0, 2, 6 2 2,, 3,, 3 3,, 3,, \ LCM of (0, 2, 6) = 2 3 = 60 d. 36, 64, 72, 96, 20 2 36, 64, 72, 96, 20 2 8, 32, 36, 48, 60 2 9, 6, 8, 24, 30 2 9, 8, 9, 2, 2 9, 4, 9, 6, 3 9, 2, 9, 3, 2 3, 2, 3,, 3 3,, 3,,,,,,,,,, \ LCM of (36, 64, 72, 96, 20) = 2 2 2 2 2 2 3 3 = 2880 TH Learning Maths 4
e. 42, 60, 84, 08 2 42, 60, 84, 08 2 2, 30, 42, 4 3 2,, 2, 27 3 7,, 7, 9 3 7,, 7, 3 7 7,, 7,,,,,,, \ LCM of (42, 60, 84, 08) = 2 2 3 3 3 7 = 3780 g. 44, 20 2 44, 20 2 72, 60 2 36, 30 2 8, 3 9, 3 3,,, \ LCM of (44, 20) = 2 2 2 2 3 3 = 720 f. 3, 7 3, 7 3 27, 3 3 9, 3 3 3, 3, 3 7, 7, \ LCM of (3, 7) = 3 3 3 7 = 472 h. 62, 270, 08 2 62, 270, 08 3 8, 3, 4 3 27, 4, 8 3 9,, 6 3 3,, 2,, 2 2,, 2,, \ LCM of (62, 270, 08) = 2 3 3 3 3 2 = 620 Exercise 6.6. LCM of 8, and 24 = 20 2 8,, 24 2 4,, 2 3 2,, 6 2 2,, 2,,,, LCM = 2 2 3 2 = 20 Smallest number = 20 3. Similar working as Q. 2. 4. We will find the HCF of 27 and 33. 27 33 27 6 27 4 24 3 6 2 6 0 3 is the largest number which divides 27 and 33. 2. LCM of 8, 24 and 36 = 72 2 8, 24, 36 3 9, 2, 8 2 3, 4, 6 3 3, 2, 3, 2, Required number = 72 + 7 = 79. Similar working as in Q 4. 46 TH Learning Maths
6. Find the HCF of 368, 480 and 36. 368 480 368 2 368 3 336 32 2 3 96 6 32 2 32 7. To find when bells will toll together, 3 9, 2, 3, 4, 8. Similar working as in Q 7. 9. 08 80 08 72 08 72 36 72 2 72 HCF of 08 and 80 is 36. Hence, 36 is the largest number of students among whom 08 chocolates and 80 cookies can be distributed equally. 6 36 33 48 6 48 8 6 2 6 \ HCF of 368, 480, 36 = 8 we need to find LCM of 9, 2 and. LCM = 3 3 4 = 80 Bells will toll together after 80 seconds, i.e., 3 minutes. Now to find the number of chocolates and cookies each students will get, divide the number of cookies and chocolates by 36. i.e., Chocolates Cookies 36 08 3 08 36 80 80 0. 4 m 2 cm = 42 cm m 0 cm = 0 cm 6 m = 600 cm 42 0 42 2 42 3 37 0 2 2 00 2 0 2 0 Hence each students will get 3 chocolates and cookies. 2 600 24 0 00 00 HCF of 42, 0 and 600 is 2. Hence, 2 cm is the length of the longest tape that can be used to measure exactly the dimensions of the given hall. TH Learning Maths 47
. ` = 00 paise `.2 = 2 paise and `0 = 000 paise Now find the LCM of 2 and 000. 2, 000 2, 000, 200, 40 8, 8, LCM of 2 and 000 = 8 =,000 Amount in paise =,000 Amount in rupees =,000 00 = `0 The number of days = `0.2 = 40 days Exercise 6.7. We know that HCF LCM = st number 2nd number 280 = 3 2nd number 2nd number = 280 3 = 40 3. HCF LCM = st number 2nd number 6 80 = 36 2nd number 2nd number = 6 80 36. LCM HCF = 2 64 92 HCF = 2 64 HCF = 2 64 92 = 4 = 30 2. HCF LCM = st number 2nd number 3 20 = 2nd number 2nd number = 3 20 = 24 4. HCF LCM = st number 2nd number 27 2079 = 89 2nd number 2nd number = 27 2079 89 = 297 6. HCF LCM = Product of the numbers LCM 6 = 432 LCM = 432 6 = 72 Test Your Skills Multiple Choice Questions. Refer answers at the end of the book. Mental Maths. 2th multiple of = 2 = 80 2. 4 782 = 4 + + 7 + 8 + 2 = 26 + = 27 is divisible by 3 and 4 782 has 2 at its end digit. So 42782 is divisible by 6. 3. Refer answer at the end of the book. 4. LCM = 73 7 = 0. Odd numbers between 0 and 00 are, 3,, 7, 9, 6, 63, 6, 67, 69, 7, 73, 7, 79, 8, 83, 8, 87, 89, 9, 93, 9, 97, 99. So, there are 2 odd numbers between 0 and 00. 48 TH Learning Maths
Apply Your Skills Problem Solving Assessment. LCM of 4 and 6 = 2 The number divisible by 2 = 3900 2 = 39048 390486 is divisible by 2 (both 4 and 6) So, 2 is the required smallest number. 2. Distance = 00 km Petrol pump is at a distance after every km. 00 6 Number of petrol pumps = 00 = 6 90 0 Petrol pumps are at a distance of km, 30 km, 4 km, 60 km, 7 km and 90 km. 3 petrol pumps are between 4 km and 00 km. 3. LCM of, 30 and 7 = 0 seconds = 2 min 30 seconds The lights will change at 8:02:30 am. 4. 036 = 03 347 2 = 34 633 3 = 630 Now find the HCF of 34, 630 and 03. 34 630 34 28 34 28 60 28 4 240 4 60 4 4 3 4 2 3900 324 36 30 24 6 60 0 48 2 03 69 90 3 3 is the greatest number that divides 036, 347 and 633 leaving remainders, 2 and 3 respectively. Value Based Questions. To find the common room, we take the LCM of 4, and 6. LCM = 2 2 3 = 60 Multiples of 60 are 60, 20, 80 and 240. Common rooms are numbered 20, 80 and 240. Value: Care for elders. 2. Amount kept to buy pens: Shubham = `00 00 = `400, Pinky = `800 00 = `700 and Rahul = `00 00 = `000 TH Learning Maths 49
HOTS To find the equal number of pens, we need to find the HCF of 400, 700 and 000. 400 700 400 300 400 300 00 300 3 300 HCF of 400, 700 and 000 = 00 00 000 0 00 0 0 a. Each can buy 00 pens. b. Shubham, as he has least money among the three and each pen costs `400 00 = `4 c. Value: Care for poors. 3. HCF of 72 and 48 = 2 2 2 3 = 24 72 = 2 2 2 3 3 48 = 2 2 2 2 3 2 72 2 36 2 8 3 9 3 2 48 2 24 2 2 2 6 3 24 rows are possible if each number has the same number of plants. Value: Health awareness. 2 0 2 0 TH Learning Maths
7 CHAPTER Fractions Lesson Plan OBJECTIVES The students should know about (i) Fractions and its parts (ii) Type of fractions (iii) Equivalent fractions (iv) Ascending and descending order of fractions (v) Addition and subtraction of fractions (vi) Degree of closeness of fractions (vii) Word problems Prerequisite Knowledge: The students should have the basic knowledge of numerator and denominator of a fraction and the type of fractions as they have studied in their previous classes. Teaching Aids: Writing board, marker, chalks, chart, duster, geometrical box, smart-board/ projector and the pointer. Method of Teaching: The following sub-topics of this chapter will be taught in the class taking some simple examples. (i) Fraction: Having numerator in upper part and denominator in lower part. For example, 3, 2 3 7,, 2, etc. (ii) Type of Fractions (a) Simple fraction: Numerator is less than the denominator, e.g., 2 3, 2 7, 9, etc. It is also known as proper fraction. (b) Improper fraction: Numerator is greater than the denominator. For example, 7 3,,, etc. 2 3 (c) Mixed fraction: A combination of whole number and a proper fraction is called mixed fraction. For example, 2 2, 3 7, 8, etc. (iii) Equivalent fractions: Which represent the same value. 2 4 For example, 3, 6 6, 9, etc. Order of Fractions For example (iv) Arrange the fractions in ascending order 2, 3 6, 4 LCM of 2, 6 and 4 = 2 6 6 2 0 3 3 9 \ 2 6 = 2, 6 2 = 2, 4 3 = 2 TH Learning Maths
2 So, the ascending order is 3 2 < 4 < 6. Recapitulation: The whole chapter will be revised in the class taking some easy examples and the problems of the students will be solved accordingly. (A) From Textbook Home Assignments (i) Exercise 7. Solve Q. No. and 2 all parts. (ii) Exercise 7.2 Solve Q. No. to all parts. (iii) Exercise 7.3 Solve Q. No. to 3 all parts. (iv) Exercise 7.4 Solve Q. No. to 3 all parts. (v) Exercise 7. Solve Q. No. and 2 all parts. (B) Extra Questions (i) Simplify: 4 3 + 4 2 (ii) Write in ascending order: 2, 3, 4, (iii) Simplify: 2 4 3 2 + 3 Exercise 7.. 2. Refer answers at the end of the book. 3. a. b. 8 7 = Quotient Remainder Divisor 37 6 = 6 6 Textbook Solutions = 2 4 7 6 37 6 36 c. f. Similar working as above. 4. a. 2 4 (2 ) + 4 = = 0 + 4 = 4 9 c. 0 e. 8 = ( 0) + 9 0 = ( 8) + 8 = 0 + 9 0 = 8 + 8 = 9 0 = 3 8 b. 3 7 9 7 8 2 4 4 = (3 9) + 7 9 = 27 + 7 9 = 34 9 d. ( 9) + = = 4 + = 46 9 9 9 9 f. 3 3 4. a. Fraction of the team played the match = b. i. Fraction of students like cricket = 2 60 = (3 4) + 3 4 = 2 + 3 4 = 4 No. of players allowed to play Total players No. of students who like cricket Total number of students ii. Fraction of students who like football = 48 60 = 4 ( 60 2 = 48) = 6 = TH Learning Maths
Exercise 7.2. Equivalent fractions are obtained by multiplying the numerator and denominator of the given fraction by the same number. a. 4 4 4 = 4 6 ; 4 = 20 ; 6 4 6 = 6 24 b. 4 4 = 4 20 ; = 2 ; 6 6 = 6 30 c. 4 8 4 = 4 32 ; 8 = 40 ; 6 8 6 = 6 48 d. 4 9 4 = 4 36 ; 9 = 4 ; 6 9 6 = 6 4 2. Refer answers at the end of the book. 3. In like fractions, the fraction with greater numerator is greater. a. 3 8 < 8 b. 4 > 9 4 TH Learning Maths 3 c. 2 > 7 d. In a given pair of fractions, whose numerators are same, the fraction with greater denominator is smaller. \ 2 7 > 2 9 e. 4 7 4 8 7 \ 4 8 32 < 3 < 7 f. 3 8 4 = 3 4 3 g. Since = 3 = 3 h. Convert unlike fractions into like fractions by finding LCM of 9 and 2. 3 9, 2 3 3, 4 4, 4, Now 9 = 4 9 4 = 20 36 20 36 > 36 4. a. LCM of and 30 = 30 LCM = 3 3 4 = 36 and or 2 = 3 2 3 = 36 9 > 2 3 = 3 2 2 = 26 30 Yes, both the fractions are equivalent. b. LCM of 6 and 4 = 4 4 6 = 4 9 6 9 = 36 4 Yes, both the fractions are equivalent. c. e. Similar working as above.. a. Equivalent fraction of 4 with denominator = 4 = 20 b., c. and d. Similar working as above.
4 6. a. Equivalent fraction of 84 84 4 with numerator 2 = 2 2 4 = 2 28. 7. a. Since the denominators are same, we arrange the numerator from smallest to greatest. 6 < 2 6 < 4 6 < 6 c. Since the numerators are same, we arrange the denominator from greatest to smallest. 38 < 34 < 26 < 22 e. LCM of 3, 4, and 2 = 2 3 2 = 60 2 3, 4,, 2 2 3, 2,, 3 = 2 20 3 20 = 40 60, 3 4 = 3 4 = 4 60 4 = 4 2 2 = 48 60, 2 = 30 2 30 = 30 30 60 60 < 40 60 < 4 60 < 48 60, i.e., 2 < 2 3 < 3 4 < 4 b., d. and f. Similar working as above. 8. a. Since the denominators are same, we arrange the fraction from largest to smallest. 3 4 > 4 > 9 4 > 3 4 b. Since the numerators are same, we arrange the denominators from smallest to largest. 0 > 0 2 > 0 3 >0 e. LCM of 4, 8, 6 and 24 = 2 2 2 2 3 = 48 2 4, 8, 6, 24 2 2, 4, 8, 2 3 2, 2, 4, 6 4 = 3 2 4 2 = 36 48, 8 = 6 8 6 = 30 48, 2, 3 6 = 3 6 3 = 33 48, 7 24 = 7 2 24 2 = 34 48 36 48 > 34 48 > 33 48 > 30 48, i.e., 3 4 > 7 24 > 6 > 8 c., d., and f. Similar working as above. 9. Dividing 32 students in 4 equal groups, i.e., 32 4 = 8 students 3 groups of 8 students each include 3 8 = 24 students Hence, 24 students are more than 0 years old and 8 students are less than 0 years old. 7 0. Tina jumped = 4 2 ft or (4 2) + 7 2 = 2 ft Mina jumped = 3 (3 6) + ft or = 8 + = 9 6 6 6 6 ft Changing both fractions into like fractions, 9 6 = 9 2 = 38 and 6 2 2 2 Since 2 > 38 2 or 4 7 2 > 3 6. Hence, Tina jumped farther. Alternative Method: Since the whole number 4 is greater than 3. 7 4 2 > 3. Tina jumped farther. 6 TH Learning Maths
Exercise 7.3 3. a. 6 = 3 3 6 3 = 2 d. g. b. 2 8 = 2 2 8 2 = 4 c. 4 7 = 4 7 7 7 = 2 2 = 2 0 0 0 6 6 6 = e. = = f. = 0 0 0 64 64 6 = 4 30 30 30 = 90 90 30 = 3 h. 49 49 49 = 98 98 49 = 2 2. To reduce the fraction in lowest fraction, we divide the numerator and denominator by common factor. The process is continued till the common factor of numerator and denominator is. a. 0 = 0 = 2 3 d. 60 96 = 60 6 96 6 = 0 2 6 2 = 8 g. 3. a. d. Exercise 7.4 b. 39 39 3 = 6 6 3 = 3 e. 66 66 = 99 99 = 6 3 9 3 = 2 3 36 340 = 36 4 34 7 = 340 4 8 7 = 2 3 h. 26 = 3 3 26 3 = 4 9 72 9 = 8 2 4 = 2 2 4 2 = 2 2 6 = 2 4 6 4 = 3 4 6 b. 20 = 6 2 20 2 = 3 0 e. 20 2 = 20 2 = 4 c. 42 6 = 42 7 6 7 = 6 2 8 2 = 3 4 98 98 4 f. = 26 26 4 = 7 9 300 300 0 i. = 480 480 0 = 30 6 48 6 = 8 c. 24 72 = 24 8 72 8 = 3 3 9 3 = 3 4 f. 6 = 4 4 6 4 = 4. a. 7 + 3 = 7 3 b. + 8 9 = 8 9 When we have like fractions, we simply add numerators, keeping the denominator same. c. + 3 = + 3 = 8 8 d. + 7 = 8 + 7 = or e. 8 + 3 6 LCM of 8 and 6 = 6 2 8, 6 2 4, 8 2 2, 4 8 2 2 = 0 and 3 6 6 = 3 6 = 3 6, 2 0 6 + 3 0 + 3 = = 3 6 6 6 = 7 LCM = 2 2 2 2 = 6 6 f. j. Similar working as above. k. 4 3 + 2 3 + 3 = 4 + 2 + = 3 3 l. 7 6 + 8 + 2 LCM of 6, 8 and 2 = 6 2 6, 8, 2 7 2 8, 4, 6 = 7 6, 8 2 2 = 0 6, 2 4, 2, 2,, 2 8 8 = 8 LCM = 2 2 2 2 = 6 6 TH Learning Maths
7 6 + 0 6 + 8 6 = 7 + 0 + 8 = 2 6 6 = 9 6 m. n. Similar working as above 2. a. 2 3 + 7 = (2 + 7) + 3 = 9 + 3 = 9 3 b. 6 + 4 2 9 = (6 + 4) + 2 9 = 0 + 2 9 = 0 2 9 When denominators are not same, we change them into like fraction by LCM method. c. + 3 = + + 3 = + + 3 = + 4 = 4 d. 3 + 32 3 = 3 + 3 + 2 3 = + 9 + 2 = 2 3 3 = 4 e. 8 + 7 3 4 = 8 + 7 + 3 4 = + 3 4 = 4 + 3 = 63 4 4 = 3 4 f. 4 + 7 22 = 4 + + 7 22 = 4 + 0 + 7 22 = 4 + 7 22 = 4 7 22 g. 3 2 9 + 8 6 = (3 + 8) + 2 9 + 6 Since LCM of 9 and 6 is 8. 6 = 3 6 3 = 3 8 and 2 9 = 2 2 9 2 = 4 8 4 Now 2 + 8 + 3 8 = 2 + 7 8 = 2 7 8 h. 7 + 9 + 27 2 = 7 + 7 3. a. Part of cake eaten by Satish = 4 9 = 7 + 82 7 = 7 + 7 7 = (7 + ) + 7 2 = 8 7 7 Part of cake eaten by his sister Anshu = 2 9 Total part of the cake eaten = 4 9 + 2 9 = 4 + 2 = 6 9 9 Changing 6 into lowest form. 9 6 3 9 3 = 2 is the total part of the cake eaten. 3 b. Fraction of money spent on books = 2 Fraction of money spent on snacks and drinks = 4 Total fraction of money spent = 2 + 4 LCM of 2 and 4 is 4 2 = 2 2 2 = 2 4 Now, 2 4 + 4 = 3 4. c. Part of book read on Monday = 4 9 Part of book read on Tuesday = 2 9 6 Part of book read on Wednesday = 9 Part of the book finished reading = 4 9 + 2 9 + 9 = 4 + 2 + = 7 9 9 TH Learning Maths
d. Weight of apples purchased = 2 2 kg Weight of grapes purchased = 3 4 kg Total weight of fruits purchased = 2 2 + 3 4 LCM of 2 and 4 is 4. 2 = 2 2 2 = 2 4 Now, 2 2 4 + 3 4 = (2 + 3) + 2 4 + 4 = + 3 4 = 3 4 kg. e. Distance jogged on Monday = 2 3 km Exercise 7. Distance jogged on Tuesday = 6 km Distance jogged on Wednesday = km 3 3, 6, 9 9, 2, 3 2 Total distance jogged = 3 + 6 + km LCM of 3, 6 and 9 = 3 2 3 = 8 9 2 + 3 + 0 = = 2 8 8 km= 7 8 km. a. 8 9 8 = 8 9 9 = 72 9 72 9 9 = 72 = 67 9 9 b. 8 = 88 8 8 or 7 4 9 as = 8 8 = 88 8 = 83 8 or 0 3 8 c. 7 9 4 9 Since fractions are like fractions, we simply subtract the numerators and write the difference over the common denominator. i.e., 7 4 = 3 9 9 or 3 3 9 3 = 3 d. 7 9 7 = 9 = 6 7 7 e. 9 4 2 9 or 7 4 4 4 = 9 4 4 = 4 2 7 = 2 2 7 2 = 4 4 f. g. Similar working as above. h. 8 or 4 8 Here, = 8 8 = 88 8 88 8 4 8 = 88 4 8 = 43 8 or 3 8 TH Learning Maths 7
i. 4 6 9 4 Here, or 4 7 4 = = 4 4 7 4 7 = = 79 or 7 2 j. 2 3 4 4 = 2 + 3 4 4 = 2 + 3 = 2 + 2 4 4 = 2 2 or 2 4 2 k. 9 2 7 6 7 We subtract the whole number and fractions separately. = (9 6) + 2 7 7 = 3 + 2 = 3 + 7 or 3 7 7 7 7 l. 8 3 9 6 4 Changing mixed numbers into improper fractions. 8 3 9 = 7 9 and 6 4 = 34 LCM of 9 and is 4. 7 9 = 37 34 9 and 4 9 = 306 4 Now, 37 4 306 37 306 = = 69 or 24 4 4 4 4 or 8 m. 3 7 2 2 4 9 Changing into improper fractions. 2 4 9 = 22 and 3 7 9 2 = 43 2 LCM of 9 and 2 is 36. 22 9 = 22 4 9 4 = 88 36 and 43 2 = 43 3 2 3 = 29 36 Now, 29 36 88 29 88 = = 4 or 36 36 36 36 n. 7 3 4 3 or 3 4 3 3 Here, = 3 4 4 = 2 4 3 4 2 3 2 = = 9 or 4 3 4 4 4 4 2. a. Sohan ate of a cake and Mohan ate of a cake. 6 Comparing the two fractions, 6 = 6 >. Hence, >. Sohan ate more. 6 8 TH Learning Maths
Changing fractions into equivalent fractions, = 6 6 = 6 30 and 6 = 6 = 30 Now, 6 30 30 = 6 30 = 30 Sohan ate more by of the cake. 30 b. Fraction of pizza Rahul has = 2 3 Fraction of pizza Abhay has = 2 Changing into like fractions, LCM of 3 and 2 = 6 2 3 = 2 2 3 2 = 4 and 6 2 = 3 2 3 = 3 6 Since 4 > 3. 4 6 > 3 6 Rahul has more pizza. (i) True (ii) False (iii) False c. Total length of pipe = 2 3 08 m or m. Length of pipe cut off from it = 0 m or 0 m. Remaining length of the pipe = 08 0 m. Changing into like fractions, 08 = 08 2 2 = 26 0 26 0 26 m = 0 0 m = 6 0 m or 6 0 m or 6 2 m d. 7 4 3 4 = 29 4 9 (29 ) (9 4) = 4 4 76 = = 69 20 20 = 3 9 20 7 2 9 3 = 3 2 28 3 (3 3) (28 2) = 2 3 0 6 = = 49 6 6 = 8 6 Since 8 > 3. 8 6 > 3 9 20 Hence, 7 2 9 is greater. 3 e. Fraction of black marbles = 3 Fraction of white marbles = 2 Fraction of marbles not green = 3 + 2 = ( 2) + ( 3) 3 2 = 2 + 3 6 = 6 Fraction of green marbles = 6 = 6 TH Learning Maths 9
Exercise 7.6. a. Subtracting 9 from 9, i.e., 9 9 = 4 9 Again subtracting 9 from 4 9. 4 i.e., 9 9 = 3 or 9 3 Hence, degree of closeness of 9 to is 2. 3 b. Subtracting 6 from 6. i.e., 6 6 = 4 6 Again subtracting 6 from 4 6. 4 i.e., 6 6 = 3 6 Hence, degree of closeness of 6 to 3 is 2. 6 c. Subtracting from 4. 4 = 4 = 3 Again subtracting from 3. 3 = 3 = 2 Again subtracting from 2. 2 = Hence, degree of closeness of 4 to is 3. d. Subtracting 8 from 7 8. 2 3 4 8 4 8 3 7 8 8 6 8 8 8 Hence, degree of closeness of 7 8 to 3 is 4. 8 2. a. To find degree of closeness of 3 8 to 2. Add 8 to 3 8, i.e., 3 8 + 8 = 4 or 8 Hence, degree of closeness of 3 8 to is. 2 To find degree of closeness of 3 8 to 4. Subtract 8 from 3 8. 3 i.e., 8 8 = 2 or 8 Hence, degree of closeness of 3 8 to is. 4 4 8 8 As degree of closeness is same in both cases. 3 8 is equally closer to 2 and 4. b. To find degree of closeness of 7 6 to 2, we add 6 to 7 6. i.e., 7 6 + 6 = 8 6 or, hence it is. 2 2 60 TH Learning Maths
To find degree of closeness (DOC) of 7 6 to 4, we subtract 6 from 7 6 i.e., 7 6 6 6 6 6 4 6 6 6 or 4 Hence, DOC is 3. We can say 7 6 is closer to 2 than to 4. c. To find DOC of 2 to 3, we subtract 3 from 2. i.e., 2 2 = 4 2 or 3 Hence, DOC =. To find the DOC of 2 to 2 3, we add 2 to 2. i.e., 2 + 2 6 2 Hence, DOC is 3. + 2 7 + 2 8 2 2 or 2 3 So, we can say that 2 is closer to 3 than to 2 3. d. To find DOC of 6 to 2, we add 6 to 6. i.e., 6 + 6 = 2 + 6 3 6 6 or 2 Hence, degree of closeness is 2. To find DOC of 6 to 3 we add 6 to 6. i.e., 6 + 6 = 2 or 6 3 Hence, DOC is. So, we can say that 6 is closer to 3 than to 2. Exercise 7.7. a. 4 + 4 + 4 + 4 + 4 = + + + + = 4 4 or 4 b. 3 + 3 + 3 + 3 + 3 = + + + + = 3 3 or 2 3 c. 3 + 3 + 3 + 3 + 3 = 3 + 3 + 3 + 3 + 3 = = 3 d. 8 + 8 + 8 + 8 = + + + = 20 8 8 = 2 4 8 or 2 2 TH Learning Maths 6
Exercise 7.8. a. c. e. 6 30 = = 2 b. 6 8 32 = 6 4 = 24 2 9 8 = 2 2 = 4 d. 8 40 = 3 8 7 = 3 7 = 2 8 8 or 2 2 f. 8 7 8 = 6 7 or 2 2 7 g. 4 7 9 = 4 9 = 36 7 7 or 7 2. a. week = 7 days 7 of a week = 7 days = day 7 b. Denominator = 4, Numerator = h. 6 2 = 6 2 = 2 or 2 2 Exercise 7.9. a. Hence, fraction = 4 c. Numerator =, Denominator =? Since the fractions is equivalent to 4 Hence, denominator = 70 4 = 70 d. Numerator =, Denominator = 4 = 4 (In case of numerator = 3, denominator = 4 3 = 2 which is not a -digit number) c. e. Hence, fraction is 4. 2 3 of = 2 3 = 0 3 = 3 3 3 4 of 2 = 3 4 6 2 6 of 7 = 2 b. 2 3 = 9 d. 3 7 = 6 3 = 3 f. 3 8 of 4 = 3 4 = 3 8 2 = 2 2 4 of 0 = 4 0 of 0 = 0 2. a. 2 3 = 2 3 = 2 3 4 b. = 4 9 3 3 = 4 d. 2 3 22 = 2 27 9 9 = 2 e. 9 3 = 3 = 3 f., g. h. Similar working as above. 3. a. 7 = 7 26 = 7 26 = 82 or 36 2 b. 2 3 3 4 = 3 2 = 3 = 4 4 c. 3 6 = 23 = 23 = or 7 6 2 2 2 2 0 2 = 4 2 = 8 0 = c. 6 7 = 7 0 2 2 62 TH Learning Maths
d. 4 3 2 = 23 2 = 23 2 = 23 0 or 2 3 0 e. 2 3 7 3 = 7 3 7 3 = 7 7 3 3 = 49 9 or 4 9 f. 2 7 9 = 27 3 7 = 3 7 9 = 2 or 4 g. 3 9 3 4 = 32 8 7 = 8 7 = 6 or 6 2 9 4 9 9 9 h. 4 2 6 2 8 = 4 3 2 8 3 7 2 = 3 7 3 8 8 = 9 8 i. 6 2 3 7 = 32 26 = 832 or 2327 7 3 3 j. 0 2 3 7 8 = 32 4 7 = 4 7 3 8 3 = 28 or 9 3 3 4. a. Total students = 0 or 3 8 Fraction of girls = Number of girl students = of 0 = 0 0 = 0 girl students b. Total number of pages = 20 Fraction of book read = Number of pages read = of 20 = 20 0 = 0 pages Number of pages left = (20 0) pages = 200 pages c. Sweets bought = 8 of kg = 8 kg Fraction of sweets Jessica ate = Amount of sweets she ate = of 8 kg = 8 = 8 = 000 g = 2 g 8 d. Earning in a month = `0,000 Fraction spent on house rent = Money spent on house rent = of `0,000 = 0, 000 2000 = `2,000 Fraction of earning spent on personal expenses = 2 TH Learning Maths 63
Money spent on personal expenses = of `0,000 2 = 2 e. Perimeter of park = 2 3 km or 7 3 km Number of rounds taken = 3 Total distance run by the boy = f. Number of bags received = 2 7 3 3 Fraction of bags containing vegetables = 2 0, 000 000 = `,000 = 7 km Number of vegetables bags = 2 of 2 = 2 2 6 = 6 bags Fraction of potatoes in vegetable bag = 7 Number of potato bags = 7 of 6 = 7 6 8 = 8 bags Exercise 7.0 9. a. b. 4 2 or 29 c. d. 4 e. 3 f. 4 3 2 49 2. a. MI of 6 is b. MI of 00 is 6 00. c. MI of 9 4 is 4 9. d. MI is 4 9. e. 2 3 = 7 3. Hence Multiplicative Inverse (MI) of 7 3 is 3 7. f. 2 3 8 = 3 6 3 8 24 = 2 \ MI of 24 is 24. g. 2 2 3 4 2 0 7 = 8 30 80 = 3 7 7 MI of 80 7 is 7 80. h. 9 2 3 4 3 = 29 3 3 3 = 377 377. Hence, MI of 9 9 is 9 377. Exercise 7.. a. 2 = 2 2 2 = 0 We have successively subtracted from and 2 time. 2 2 = 2 2 = 2 b. 3 = 2 2 3 3 3 = 2 3 3 3 = 0 3 3 = 3 or 3 = 3 c. 2 2 = 2 2 2 = 2 64 TH Learning Maths
2 = 3 2 2 2 = 0 4 Hence, 2 = 4 or 2 2 = 4. 2 d., e. and f. are done in the same manner. 2. a. Repeatedly subtracting from 4, we get 4 4 4 = 33 4 3 3 4 4 = 32 4 3 2 4 4 = 3 4 3 4 4 = 3 3 4 = 23 4 2 3 4 4 = 22 4 2 2 4 4 = 2 4 2 4 4 = 2 2 4 = 3 4 3 4 4 = 2 4 2 4 4 = 4 4 4 = 4 = 3 4 3 4 4 = 2 4 2 4 4 = 4 4 4 = 0 We have successively subtracted from 4, i.e., 6 times. 4 \ 4 4 = 6 b. Repeatedly subtracting from 3, we get 3 3 3 = 22 3 2 3 = 2 3 3 = 2 3 2 2 3 3 = 2 3 2 3 3 = 3 2 3 3 = 3 2 3 3 = 2 3 3 = 3 3 = 0 We have successively subtracted from 3, i.e., 9 times. 3 \ 3 3 = 9 c. and d. Similar working as above. Exercise 7.2. a. 2 3 = 2 3 = 2 3 = 6 b. 9 0 9 = 9 0 9 = 9 0 9 = 9 90 ( reciprocal of 3 is 3 ) c. 3 8 6 = 3 = 8 6 6 d. 2 4 = 3 2 = 3 = e. 24 0 4 3 = 2 3 24 = 0 2 2 3 = 6 f. 8 7 9 = 8 9 7 = 4 6 h. 24 2 2 = 24 2 2 = 288 2 = 2 38 2 j 27 8 3 8 = 27 7 8 8 9 = 3 7 9 = 99 g. 2 3 4 = 4 = = 2 3 3 9 = 2 9 i. 36 4 8 3 = 9 36 = 3 4 8 2 = 3 2 or 3 2 TH Learning Maths 6 7 33
k. 6 = 0 0 6 = 60 m. 2 4 6 3 7 = 9 7 = 3 7 4 6 4 2 = 2 8 or 2 8 n. 4 4 7 = 24 7 = 72 7 = 0 2 7 p. 4 4 4 3 8 = 7 8 = 34 4 3 3 r. 7 3 7 4 4 = 2 22 4 = 2 2 = 4 7 6 2. a. Total sugar = kg 2 2 3 2 l. 3 2 3 6 = 3 6 = 8 o. 2 3 4 3 7 2 = 2 = 7 3 = 4 3 q. 2 3 6 8 = 7 3 8 = 7 2 6 4 8 3 9 Sugar in packet = 7 of = 7 = 7 Number of packets = 7 = 7 = 7 b. 4 of the distance covered in 8 minutes. 9 Total time taken to reach the house = 8 4 9 minutes = 2 9 8 = 8 minutes 4 c. Sweets distributed to children = 000 kg = = 20 g 4 4 Each child will get = 20 g = 0 20 = 0 g 3 d. 2 9 84 9 7 3 4 = 3 84 9 7 9 3 2 9 3 4 = 3 4 = 2 2 = 2 e. ` = 00 paise `3.0 = 3.0 paise `0 = 000 paise 7 30 Hence, the fraction is = 7 000 20. 20 f. Cost of 6 2 3 kg of rice = `24 2 3 or ` 74 3 Cost of kg of rice = 74 ` 3 6 2 3 = 74 ` 3 = 37 ` or ` 3 7 0 0 37 3 20 0 Test Your Skills Multiple Choice Questions.. Refer answers at the end of the book. 66 TH Learning Maths
Riddles. Total pizzas eaten = 3 3 4 + 8 3 4 = 4 + 3 4 = 0 4 = 2 2 = 2 2 pizzas 2. 2 2 2 2 2 2 2 2 2 2 = 0 times 2 3 4 3. Quantity of flours in 2 4 grams = 9 000 mg = 220 mg 4 3 cups of flour = 220 = 220 3 = 70 mg 3 Apply Your Skills Problem Solving Assessment 4. Fractions representing green = = 0, blue = 20 20 = 3 20 4 0 6, red = = 2 20 20 0 Fractions of the balls representing geen, blue and red are, 2, 3 0 respectively. = 3 0 Fractions from greatest to smallest = 2, 3 0, 2. Cloth left = 9 3 6 2 2 + 4 4 = 47 6 2 + 7 4 = 47 6 27 47 08 = = 39 4 6 6 = 2 7 6 m 3. Refer answers at the end of the book. 4. First complete the figure. Now, fraction of shaded part = 2 32 or 6 Value Based Questions. Chocolate distributed = 2 + 8 + 4 = 4 + + 2 = 7 8 8 Chocolate left = (whole) 7 8 = 8 7 = 8 8 Number of chocolates = 24 8 or, Number of chocolates bought = 24 8 = 92; Value: Social values 2. Number of packets = 6 4 = 64 packets (4 one-fourth make kg, so 64 one-fourth make 6 kg.) Number of plants in the garden = 64 8 = 2 plants; Value: Care for nature TH Learning Maths 67
HOTS. a. Son s share = 20 = 4 camels b. Daughter s share = 20 = camels 4 c. Wife s share = 20 = camels 4 Thus, 4 + + = 4 camels are distributed and 8 camels are left with Setu. Mental Maths 2 2. 3 2 = 4 6 2. Fraction = 2 + 3 4 = 20 3. Fraction = 3 2 2 3 = 9 4 = 6 6. 4. Smallest twin primes are 3 and. 4 4,, 3 + + = 4 6 = 2 3. So, fraction is to be 3.. week = 7 days = 7 24 hours = 7 24 60 minutes = 7 24 60 60 seconds 60 60 7 24 60 60 = 24 seconds 7 8 CHAPTER Decimals and Percentage Lesson Plan OBJECTIVES The students should know about (i) Decimals and parts (iii) Fractions to decimals (v) Like and unlike decimals (vii) Ordering of decimals (ix) Word problems (ii) Decimals on place value chart (iv) Decimals to fractions (vi) Equivalent decimals (viii) Operation on decimals (x) Applications of decimals Prerequisite Knowledge: The students should have the basic knowledge of decimals as they have already studied in their previous classes. Teaching Aids: Writing board, marker, chalks, charts, duster, geometrical box, smart-board/ projector and the pointer. 68 TH Learning Maths
Method of Teaching: The following topics and subtopics of this chapter will be taught in the class. (i) = one-tenth part = 0. 0 00 000 = one-hundredth part = 0.0 = one-thousandth part = 0.00 (ii) Decimals on place value chart (iii) Expanded form (iv) Fraction to decimals Th H T O t h th (000) 0 0 0 0 (00) 0 0 0 (0) 0 0 () 0 28.49 = 20 + 8 + 4 9 + 0 00 3 2 = 3 = =. 2 0 7 8 = 7 8 2 87 = = 0. 87 2 000 (v) Addition, subtraction, multiplication and division of decimals will be explained on the board by taking some examples. Recapitulation: The whole chapter will be revised in the class by involving the students and the problems of the students will be solved immediately. (A) From Textbook Home Assignments (i) Exercise 8. Solve Q. No. to 4 all parts. (ii) Exercise 8.3 Solve Q. No. to 4 all parts. (iii) Exercise 8.6 Solve Q. No. to 2 all parts. (iv) Exercise 8.7 Solve Q. No. to 3 all parts. (B) Extra Questions (i) Write the following decimals in expanded form. (a) 38.26 (b) 7.023 (c) 6.6 (ii) Find the quotient. (a) 6.64 2 (b) 3.7 (c) 26.38 2 TH Learning Maths 69
Exercise 8... Refer answers at the end of the book. Exercise 8.2. a. Textbook Solutions 7 00 = 0.07 b. 7 3 0 = 7 + 3 = 7 + 0.3 = 7.3 0 7 c. 4 00 = 4 + 0.07 = 4.07 d. 2 3 = 2 + 0.003 = 2.003 000 e. 4 = 4 2 2 = 8 = 0.8 0 4 f. 2 = 4 4 2 4 = 6 00 = 0.6 g. 2 0 = 2 2 0 2 = 42 00 = 0.42 h. 8 2 = 8 8 2 8 = 64 000 = 0.064 i. 3 2 = 3 2 = 6 0 = 6. j. 2 = + 4 4 2 =.2 k. 7 2 = 7 + 2 2 2 = 7 + 4 0 = 7.4 l. 3 8 = 3 + 2 8 2 = 3 + 2 000 = 3.2 4 2. a. 0.4 = 0 + 0 = 2 c. 0.9 = 0 + 9 00 = 9 00 2 b. 3. = 3 + 0 = 3 + 2 d. 3.2 = 3 + 2 00 2 or 3 2 or 3 2 00 34 e. 6.34 = 6 + = 6 7 00 0 0 i. 7.0 = 7 + 0 or 7 0 000 000 7 f h. Similar working as above. j. 78.9 = 78 + 9 9 = 78 000 000 Exercise 8.3. Decimals having equal number of decimal places are called like decimals. a. (3.4, 4.0); (8.3, 39.9) b. (2., 3.7); (44.632, 0.49) c. (8.43, 9.87); (6.009, 8.4) d. (.2,.689); (8., 9.8) 2. In order to convert a group of decimals into like decimals, we make the number of digits to the right of decimal point in all of them same by adding required number of zeros. This is done as adding any number of zeros after the extreme right digit in the decimal number does not make any change to its value. a. Since.738 has maximum 3 decimal places. the required like decimals are:.00,.738, 2.0 b. Since 39.8 has maximum 3 decimal places. the required like decimals are: 74.090, 39.8, 2.800 c. Since 0.489 has maximum 3 decimal places. the required like decimals are: 8.00, 394.260, 0.489 d. Since 30.623 has maximum 3 decimal places. \ the required like decimals are: 346.620, 439.00, 30.623 70 TH Learning Maths
3. Since adding any number of zeros after the extreme right digit in the decimal number does not make any change to its value. The equivalent fractions are: a. 6.7 = 6.700 b. 0.0 = 0.00 c. 44.89 = 44.890 4. a. 6. The equivalent fractions are 6.0, 6.00 b..80 The equivalent fractions are.8,.800 c. 9.700 The equivalent fractions are 9.70, 9.7 d..4 The equivalent fractions are.40,.400 Exercise 8.4. a. 37.7 < 37.7 (digit at tenth place is greater) b. 44.2 > 87.489 (In whole number part, 44 > 87) c. 7. = 7.00 (equivalent fraction) d. 8.34 < 80.4 (as 8 < 80 in whole part) e. 78.90 < 87.9 (digit at tens place, 7 < 8) f. 97. > 97.9 (reason same as in b) 2. a. Lowest = 4.30 (4 being the lowest whole number) Highest = 43.0 (greatest digit in tens place) b. Lowest = 46.267 Highest = 764.26 c. Lowest = 27.44 (minimum digits on left side of decimal) Highest = 274.4 (maximum digits on left side of decimal) d. Lowest = 46.2478 (same reason as above) Highest = 478.426 3. By comparing the digits one by one, the ascending order will be: a. 8.06 < 8.60 < 80.6 < 86.0 b. 44.76 < 46.47 < 46.74 < 47.64 c. 9.067 < 90.67 < 96.07 < 97.60 d. 2.673 < 2.763 < 6.724 < 7.624 4. By comparing the digits one by one, the descending order will be: a. 60.68 > 60.08 > 6.80 > 6.008 b. 90.3 > 9.03 > 3.09 > 0.93 c. 46.23 > 46.23 > 42.63 > 4.623 d. 4.448 > 4.442 > 4.440 > 4.404 Exercise 8.. Write or arrange the numbers with decimal points below one another. a. 2 7. + 0.3 2 7.4 b. 4 2.8 6 + 2 0. 3 6 2.9 9 c. 7.2 4 + 2 3.4 2 0 8 0.6 6 d. 4 6.4 0 + 3 2 2. 2 8 3 6 8. 2 9 e. 8 2.3 6 9 + 0 0.7 7 8 3. 4 0 f. 2 6.6 0 0 0.0 0 4 + 4.6 8 2 2.2 8 g. 6 4. 2 4.0 0 + 2 3.7 3 0.8 3 h. 2 8.0 7 4 0.6 6 0 +.4 4 4 4. 7 9 TH Learning Maths 7
2. Numbers are put in columns with the larger number on top and the decimal point. Underneath are another empty place values are filled with zeros so that all the number have same number of decimal places. a. 7.6.4 6.2 e. 2.9 9 3 2.2 8 0 0.7 3 Exercise 8.6 b..2 0. 0. f. 0 6 0 2. 7 0.3 8 7 0.7 8 3 c. 2 7. 8 0.2 2 2 7.3 6 g. 4..6 2 0 0 3.9 3 d. h. 3 9 9 0 2 4 0.0 0 2 0. 4 3 8.4 6 6 9 9 0 3 7.0 0 0 0.0 3 3 6.9 6 9. When a decimal is multiplied by 0, the decimal point is shifted by place to the right. When a decimal is multiplied by 00, the decimal point is shifted by 2 places to the right. a. 4.79 0 = 47.9 b. 39.4 0 = 39.4 c. 82.483 00 = 8248.3 d. 0.6 00 = 6 e. 4.0 00 = 40.0 f. 34.9 000 = 3490 (since the number of decimal place is only 3 we add a zero) g. 436.38 000 = 43638 h. 0.008 000 = 8 i. 2.6 80 = 2.6 8 0 = 7.28 0 = 72.8 j. 7. 40 = 7. 4 0 = 70 0 = 700 k. 8.84 00 = 8.84 00 = 44.07 00 = 4407 l m. Similar working as above. n. 9.36 2000 = 9.36 2 000 = 38.730 000 = 38730 2. a. 2.7 0.6 27 6 62 The number of digits after the decimal point in the multiplicand is and multiplier is. 2.7 0.6 =.62 72 b. 7.26 4 7 2 6 4 2 9 0 4 7.26 4 = 29.04 e. 2 6 7 2 2 3 4 4 + 2 6 7 2 0 3 2 0 6 4 26.72.2 = 32.064 g. 4 6 7 3 8 3 7 3 6 4 0 0 + 4 6 7 0 0 6 4 4 4 6 c d. Similar working as above. f. Similar working as above. The number of digits after decimal point in the multiplicand = The multiplier = Total number of digits after decimal point = 2 46.7 3.8 = 644.46 TH Learning Maths
h. 6.789 0.4 6 7 8 9 4 2 7 6 i. Similar working as above. Exercise 8.7 6.789 0.4 = 2.76. When a decimal is divided by 0, the decimal point moves towards the left by place. When a decimal is divided by 00, the decimal point moves towards the left by 2 places. When a decimal is divided by 000, the decimal point moves towards the left by 3 places. a. 98 0 = 9.8 b. 234 00 = 2.34 c. 640 000 = 6.40 d. 4. 0 = 4. e. 39.6 00 = 3.96 f. 482.6 000 = 0.4826 g. 39. 000 = 0.039 (A zero is placed before first digit if the number of digits is less than the required number of decimal places.) h. 2.46 30 = 2.46 30 or 82 246 = 00 30 0 82 000 = 0.082 i. 38.4 0 = 384 00 0 2 2 = 384 2 00 00 = 7628 0000 = 0.7628 j. 4.86 200 = 243 486 = 00 200 00 243 0000 = 0.0243 k. 24. 00 = 24 0 00 2 2 = 4282 0000 = 0.4282 2. a. 8.0 3 = 6 8. 0 = 6 3 b. 6.64 2 = 2832 664 00 c. 40.96 6 = 4096 00 = 2832 2 00 = 28.32 26 024 = 26 or 2.6 6 4 00 4707 69 944 d. 88.28 2 = 8828 = 69 00 2 6 00 =.69 3 e. Similar working as above. 3 63 00 0 0 63 f. 6.300 2.0 = = = 3 0 00 20 2 g. 6.4 4.8 = 6. 0 48 0 = 4 64 0 h. Similar working as above. i. 0..4 = 0 0 48 2 7 203 = 7 4 29 = 4 2 =.7 TH Learning Maths 73
j. Similar working as above. 3 27 k. 0.337 0.2 = 337 0000 2 000 = 337 67 000 = 27 0000 2 0 l. Similar working as above. 3. a. 8 0.9 or 9 80 90 8 0 8 0 0.9 0 = 80 9 \ Quotient = 90 4620 0 c. 4620 2. = 2. 0 = 46200 2 Now, 2 46200 848 2 22 200 20 00 200 200 \ Quotient = 848 2 00 e. 2.68 =.68 00 = 200 68 Now 68 200 32. 04 20 68 420 336 840 840 x \ Quotient = 32. 2 b. 99. = 99. or 2.7 99 0 =. 0 = 990 990 90 99 0 \ Quotient = 90 69 00 d. 69 0.23 = 0.23 00 = 6900 23 Now, 23 6900 300 69 00 00 xx \ Quotient = 300 f h. Similar working as above. Exercise 8.8. Total length of 3 pieces of wood is 2.4 6 m.3 m + 0.9 2 m 4.7 3 m 2. Money spent on icecream = `2.06 Money spent on snacks = `63.24 Money spent on movie ticket = `90.90 Total money spent = `(2.06 + 63.24 + 90.90) = `66.20 74 TH Learning Maths
3. Total length of ribbon = 6.70 m Length of the piece cut off from it = 8.4 m Length of the ribbon left = (6.70 8.4) m = 8.2 m. or 6.7 0 m 8.4 m 8.2 m 4. Initial weight = 97. kg Weight lost = 3.8 kg Present weight = (97. 3.8) kg = 83.7 kg. Length of each ribbon piece =.0 m Number of pieces = 27 Total length of the ribbon = (27.0) m = 40.0 m 6. The rate at which man worked = `0.0 per hour Number of hours worked = 30 Money earned = `(0.0 30) = `33 7. Rate of cloth = `78.0 per metre Length of cloth purchased = 2.3 m Total amount spent = `(78.0 2.3) = `80. 8. Total cloth = 8 m Cloth required for suit = 2. m Number of suit that can be made from 20 m cloth = 20 2. or 20 0 2. 0 = 20040 = 8 2 Number of suits that can be made from 20 m cloth is 8. 9. Distance covered in 6 litres = 7.6 km Distance covered in litre = (7.6 6) km = 9.8 km 0. Cost of 2. kg of sugar = `29.2 Cost of kg of sugar = `(29.2 2.) = `23.30 Cost of 3. kg of sugar = `(23.30 3.) = `8. Exercise 8.9. 0 mm = cm To convert mm into cm, we divide the given number by 0. 8 a. 49 mm = 49 48 cm or 4.9 cm b. 48 mm = cm or 4.8 cm 0 0 c. 6 cm 4 mm = 6 cm + 4 cm = (6 + 0.4) cm or 6.4 cm 0 d. 92 cm 2 mm = 92 + 2 0 cm = (92 + 0.2) cm = 92.2 cm 2. 00 cm = m To convert cm into m, we divide the given number by 00. a. 84 cm = 84 00 m = 8.4 m TH Learning Maths 7
b. 248 cm = 248 00 m = 2.48 m c. 983 m 2 cm = 983 + 2 m = 983 + 0.2 = 983.2 m 00 d. 7 m 36 cm = 7 + 36 m = (7 + 0.36) m = 7.36 m 00 3. 000 g = kg To convert g into kg, we divide it by 000. a. 84 g = 84 kg = 8.4 kg 000 b. 00 g = 00 kg =.00 kg 000 c. 7 kg 2 g = 7 + 2 kg = 7 + 0.2 kg = 7.2 kg 000 d. 2 kg g = 2 + kg = 2.0 kg 000 4. 00 paise = rupee To convert paise into rupees, we divide it by 00. a. 77 paise = `77 00 c. rupees 2 paise = ` + 2 00 d. 20 rupees 8 paise = ` 20 + = `7.7 b. 9003 paise = `9003 00 = `90.03 8 00. 000 ml = L To convert ml in L, we divide it by 000. a. 400 ml = 400 000 L = 4. L b. 0030 ml = 0030 000 L = 0.030 L = `( + 0.2) = `.2 = `(20 + 0.08) = `20.08 c. 2 L 27 ml = 2 + 27 L = (2 + 0.27) L = 2.27 L 000 d. L 0 ml = + 0 L = ( + 0.00) L =.00 L 000 6. a. `7.2 = 7.2 00 p = 72 p b. 9.00 L = 9.00 000 ml = 900 ml c..37 km =.37 000 km = 37 m d. `6.3 = 6.3 00 p = 63 p e. 2.300 L = 2.300 000 ml = 2300 ml f. 2.90 km = 2.90 000 m = 290 m g. 7. cm = 7. 0 mm = 7 mm h. 2.6 cm = 2.6 0 m = 26 mm i. 4. m = 4. 00 cm = 40 cm j. 3.08 m = 3.08 00 cm = 308 cm k. 8. kg = 8. 000 g = 80 g l..04 kg =.04 000 g = 040 g 76 TH Learning Maths
Exercise 8.0. To convert a fraction into percentage, we multiply it by 00 and put the symbol %. a. c. 3 3 2 3 20 = 00 % = 60% 3 4 = 00 % = 2% 2 b. 8 d. 3 20 2 20 8 00 00 2 = % = % = % = 62. % 8 2 4 2 23 = 00 % = % 20 e. 8 2 42 20 = 00 % = 840% 2. To convert a decimal into percentage, move the decimal point two places to the right and attach the per cent sign. a. 0.7 = 70% b. 4.6 = 460% c. 0.8 =.8% d. 64.02 = 6402% e..02 = 02.% 3. To convert percentage into fraction, we write 00 under the number. 9 33 a. 9% = b. 33% = 00 00 7 6. 6 7 82 82 2 c. 6.% = or = d. 82% = = 00 000 2 00 00 2 2 32 32 4 33 e. 32% = = = or 8 00 00 4 2 2 = 4 0 4. To convert percentage into decimals, we move the decimal point two places to the left. a. 3% = 3 = 0.3 00 8 b. 8% = = 0.8 00 2 c. 2% = 00 =.2 d. 4.% = 4. = 0.04 00 0.7 e. 0.7% = 00 = 0.07. a. 3% of 00 = 3 00 of 00 = 3 00 b. 0% of 800 = 0 00 of 800 = 0 00 c. 90% of 40 = 90 00 of 40 = 90 00 00 = 3 8 800 = 400 40 = 40 d. 20% of 62 = 20 20 00 of 62 = 00 6. a. kg = 000 g 2 62 = 2 2% of kg = 2 00 of 000 g = 2 00 0 00 g = 20 g TH Learning Maths 77
b. % of 70 m = 00 of 70 = 00 c. 40% of 00 L = 40 00 of 00 L = 40 00 d. 60% of `200 = 60 00 of `200 = 60 00 7. a. kg = 000 g kg = 000 g Now 0 g of kg = b. L = 000 ml 0 000 2 70 m = 77 2 m = 38. m 00 L = 200 L 2 00 = ` 720 00 % = % Converting 20 ml of L as a percentage 20 = 0 00 0 0 % = 2% c. ` = 00 paise `2 = 200 paise Now percentage of 0 paise of 200 paise 0 = 00 % = % 200 d. km = 000 m 6 km = 6000 m Now percentage of 300 m of 6000 m = 300 60 00 e. `2 of `400 00 = % Percentage = 2 400 00 = 3.2% 8 f. 2.4 kg of 3 kg = 24. 24 00 % = 00 % = 80% g. 36 3 3 0 0 h. 420 600 7 00 = 70% i. 30 00 j. h = 60 min 2 h = 20 min 2 Now, 2 0 00 0 % = 0% k. day = 24 h 2 2 days = 2 242 h = 60 h. Now, 4 24 60 2 00 = 72% 70 00 = 70% 00 % = 40% 78 TH Learning Maths
Exercise 8.. a. 20% of 0 = 30% of 80 = 20 0 0 30 0 0 0 2 3 0 = 30 80 = 4 Since 4 > 30. 30% of 80 is greater than 20% of 0. b. % of 300 = 00 300 = 4 2% of 200 = 2 00 200 = 24 Since 4 > 24. % of 300 is greater than 2% of 200. 2. Kartik s pocket money = `00 80 Amount he spends = 80% of `00 = ` 00 3. Maximum marks in the examination = 40 Raghav scored = 7% of 40 = 7 00 3 4 3 40 = 40 4. Ajeet s weight = 7 kg His son s weight = 60% of 7 kg =. Total fruits sold in a day = 80 kg 60 00 4 00 = `400 3 7 kg = 4 kg 30 Apples sold = 30% of 80 kg = 80 kg = 24 kg 00 6. Milk sold in a day = 2. L Water mixed in the milk = 20% of 2. L = 20 00 2. 2 2 2. = = = = 0 0 0 2 2 = 0. L or 00 ml Test Your Skills Multiple Choice Questions. Refer answers at the end of the book. Mental Maths. A.2.2.22.23.24.2.26.27.28.29.3 B TH Learning Maths 79
80 2. 6 + 00 = 6 = 6.0 (True) 00 3. 3.6 is rounded off to 3.60 = 3.6. 4. 6 out of 00 squares are shaded. So its percentage = 6 00 = 6%. Successor of 9999 = 9999 + = 0000 2 2% of the successor = 2% of 0000 = 0000 = 200 00 So, required number = 0000 + 200 = 0200 Apply Your Skills Problem Solving Assessment. a. 20 % of `2 2 % of `30 b. 6% of 6 7% of 9 20 00 2 2 00 30 6 00 6 7 00 9 2 < 7. 3.6 < 6.3 2. a. 3% of x = ` 69 3 x = 69 Alternate method: 00 x = 69 3 00 69 = ` 300 Let the total money = ` 00 00 3 ` 3 when total is ` 00. \ ` when total is ` 00 3. \ ` 69 when total is ` 00 3 69 3 = ` 300 b. % of x = ` 70 00 x = 70 x = 70 0 00 = 70 = ` 000 00 8 c. 8% of x = ` 48 00 x = 48 8 x = 48 00 = 48 6 00 = ` 600 8 80 d. 80% of x = ` 6 00 x = 6 x = 6 80 00 = 6 2 00 80 = ` 20 000 > 300 > 600 > 20 So, b > a > c > d. 3. Cloth needs for safari suit =.40 m + 2.7 m = 4. m Length of cloth gifted by Vimal s mother = 4. m 0.82 m = 3.33 m 4. Do it yourself.. Salary saved by Rishab = `3200 22 % of x = ` 3200 22 00 x = 3200 6600 600 x = 3200 00 = `60,000 (= salary of Abhay) 22 TH Learning Maths
Salary saved by Abhay = 4% of `60,000 = ` 4 60000 = `8400 00 Value Based Questions. Total amount spent by Mr. Lal = `497.0 + `2496.0 + `00 = `8972 Value: Concern for poor. 2. Saplings donated for planting across the roads = 0 % of 0000 = 0 0000 = 000 00 Saplings left = 0000 000 = 9000 Saplings donated for decorating the park = % of 9000 = 9000 = 40 00 Total saplings donated by Savita = 000 + 40 = 40 Value: Care for environment. 3. Money spent by Ravi for his family = 00 (20 + ) = 7% That means, Ravi spends `7 if his earnings is `00. He spends ` if his earnings is `00 7. He spends `000 if his earnings is ` Total earnings of Ravi = `20000 Value: Family values. 00 7 200 000 = `20000 HOTS. Money spent by Ananya in a month = `747.0 + `30.2 + `40.2 + `00 = `608.00 Money spent by Ananya for the whole year = `608.00 2 = `9296 2. Weight of suitcase = 2 3 weight of trunk = 2 3 2.60 kg = 4.4 kg Weight of bag = 0 weight of suitcase = 0 2 3 weight of trunk Total weight of suitcase and bag = 4.4 +.44 =.84 kg. = 2 30 weight of trunk = 2 2.60 kg =.44 kg 30 9 CHAPTER Simplifications and Average Lesson Plan OBJECTIVES The students should know about (i) DMAS Rule (ii) Average TH Learning Maths 8
Prerequisite Knowledge: The students should have the basic knowledge of simplification of the whole numbers as they have studied in their previous classes. Teaching Aids: Writing board, marker, chalks, charts, duster, geometrical box, smart-board/ projector and the pointer. Method of Teaching: The following topics of this lesson will be taught in the class by taking some examples. (i) DMAS: Division, Multiplication, Addition and Subtraction are used in simplification. (ii) Simplify: 40 36 9 + 3 Using DMAS, 40 36 9 + 3 = 40 4 + 3 = 40 20 + 3 = 43 20 = 23 Sum of given quantities (iii) Average = Total number of quantities Example: Find the average of the following numbers. 26, 20, 36, 48 and 60 26 + 20 + 36 + 48 + 60 Average = = 90 (iv) Word Problem: Three factories produce 90 articles, 82 articles and 9 articles respectively. Find the average production. 90 + 82 + 9 Average production = 3 = 267 = 89 articles 3 Recapitulation: The whole chapter will be revised in the class by the involvement of the students and their problems will be solved accordingly. Home Assignments (A) From Textbook (i) Exercise 9. Solve Q. No. and 2 all parts. (ii) Exercise 9.2 Solve Q. No. and 2 all parts. (B) Extra Questions (i) Simplify: + 2 3 4 6 2 (ii) Find the average of 6, 67 and 69. = 38 82 TH Learning Maths
Exercise 9.. To simplify we use the DMAS rule. Textbook Solutions a. 24 2 + = 2 + = 7 b. 6 + 3 = 6 + = c. 33 3 = = 0 d. 39 3 + 0 = 3 + 0 = 3 e. 42 6 3 = 42 2 = 84 f. 63 3 2 = 63 63 = 0 g. 00 40 = 00 8 = 92 2. We follow DMAS rule. Here, multiplication and division rank equally, and addition and subtraction also rank equally. a. 6 2 3 = 3 3 = 9 = 2 b. 30 3 + 6 3 0 = 0 + 8 0 = 28 0 = 8 c. 8 20 4 = 8 = 90 = 3 d. 4 2 7 + 4 2 = 4 3 + 8 = + 8 = 9 e. 82 42 2 2 = 82 2 2 = 82 4 = 78 f. 20 + 4 30 = 00 + 60 30 = 60 30 = 30 Exercise 9.2. a. Sum of the given quantities = 8 + 24 + 32 + 46 = 20 Number of quantities = 4 Average = Sum of given quantities Total number of quantities = 20 60 30 4 2 = 30 b. Sum of the given quantities = 36 + 0 + 4 + 77 + 83 = 300 Number of quantities = 60 Average = 300 = 60 c. e. Similar working as above. 2. a. First ten natural numbers =, 2, 3, 4,, 6, 7, 9, 0 Average = + 2 + 3 + 4 + + 6 + 7 + 8 + 9 + 0 0 b. First multiples of =, 0,, 20, 2 + 0 + + 20 + 2 Average = = 7 = c. First five composite numbers = 4, 6, 8, 9, 0 Average = 4 + 6 + 8 + 9 + 0 = 37 = 7.4 d. Marks obtained by friends = 98, 96, 84, 72, 8 Average marks = 98 + 96 + 84 + 72 + 8 = 43 = 0 =. 87 = 87 TH Learning Maths 83
84 e. Rainfall in a city for consecutive years = 200 cm, 0 cm, 240 cm, 60 cm, 77 cm, 22 cm, 6 cm, 240 cm, 60 cm, 8 cm, 20 cm Sum of rainfall in consecutive years Average = (200 + 0 + 240 + 60 + 77 + 22 + 6 + 240 + 60 + 8 + 20) cm = = 903 cm = 73 cm f. Average weight of 6 mangoes = kg Total mangoes in 7 kg = 6 7 = 02 g. Average earning of 2 persons in month = `3400 Total earning in month of 2 persons = `3400 2 = `40800 Test Your Skills Multiple Choice Questions 2 + 20 + 30 + 42 + 6. b. Average = = 20 = 24 2. d. 48 + 3 2 6 = 48 + 3 2 = 48 + 6 = 4 = 43 3. b. 3. + 2. 4 = 3. + 3.2 = 6.62 4. d. Average cost of articles = `40 Total cost of articles = `40 = `200. b. Prime numbers between to 20 = 2, 3,, 7,, 3, 7, 9 2 + 3 + + 7 + + 3 + 7 + 9 Average = = 77 8 8 = 9.62 Mental Maths. Number = (93 73) (3 + 2) = 20 = 00 33.7 + 3.0 + 43.2 + 4.0 2. Average Income = = 8 4 4 = 39.0 3. 7.2 2.9 + 4. + 2. = 7.2 2.9 + 4. + 2. = 7.2 + 6.2 2.9 = 23.4 2.9 = 20. 4. Total no. of biscuits in 6 small packets and big packet = 0 6 + = 7 Biscuits are distributed among 6 friends, dividing 7 by 6 we get 2 as quotient and 3 as remainder. Thus, each friend gets 2 biscuits and 3 biscuits are left.. Temperature in the morning = Temperature in the afternoon 3 C Temperature at night = Temperature in the afternoon 6 C \ Temperature in the afternoon = Temperature at night + 6 C Temperature in the afternoon = 6 C + 3 C = 9 C Temperature in the morning = 9 C 3 C = 6 C Total temperature = 6 C + 9 C + 3 C = 8 C Average temperature of the day = 8 C = 6 C. Problem Solving Assessment. a. 72 (3 4) = 72 2 = 6 b. 72 (7 9) = 72 63 = 9 3 24 6 7 2 6 2 3 TH Learning Maths
c. 84 (2 6) 84 72 = 2 d. 3 + (3 + 2) = 3 + 60 = 3 + 300 = 33. 2. Total sweets = 4 3 + 7 3 + 0 3 = 2 + 2 + 30 = 63 3. Total = 3 ducks A B C 4. Present population = 4000 + 2 3 8000 4000 = 4000 + 36000 = 90000 Value Based Questions. People educated on st day = 0 People educated on 2nd day = 2 0 = 20 People educated on 3rd day = 2 20 = 40 People educated on 4th day = 2 40 = 80 People educated on th day = 2 80 = 60. 0 + 20 + 40 + 80 + 60 So, Average = = 30 = 62; Value: Cleanliness 2. Total amount spent = `323.7 + 4 `67.0 + `20.7 = `68.7 + `2702 + `20.7 = `47.0, Value: Concern for needy. HOTS. a. Number of notebooks with children = 2 6 + 8 3 = 72 + 24 = 96 Notebooks left after given to the teacher = 96 60 = 36 Notebooks given to the headmaster = 36 2 = 8 Notebooks left at last = 96 (60 + 8) = 96 78 = 8 b. Toffees bought = 7 0 = 70 + 3 (free) = 73 Toffees distributed = 73 4 = 69 Number of students = 69 3 = 23 0 CHAPTER Geometry Lesson Plan OBJECTIVES The students should know about (i) Basic definition: point, line, plane (ii) Concurrent lines, intersecting lines, parallel lines and perpendicular lines (iii) Angles and their types (iv) Measurement of angles (v) Construction of angles (vi) Triangles and types of triangles (vii) Angle sum property of triangle (viii) Types of quadrilateral (ix) Circle and its properties TH Learning Maths 8