ID : pk-6-natural-and-whole-numbers [1] Grade 6 Natural and Whole Numbers For more such worksheets visit www.edugain.com Answer t he quest ions (1) Along the highway, there are electric poles on one side of the highway and telegraph poles on the other side. The electric poles are all separated by 12 m and the telegraph poles are all separated by 140 m. If an electric and a telegraph pole are both present at the point where the highway begins, af ter how much distance along the highway will they both be in f ront of each other again? Choose correct answer(s) f rom given choice (2) Ishaq wrote an exam which had 16 questions. Each question he answers correctly gets him 10 marks. However, he loses 5 marks f or each question he answers incorrectly. He attempted all the questions and got a total of 130 marks. How many questions did he answer wrong? a. 0 b. 5 c. 2 d. 7 (3) Find LCM of 3/2 and 1/3. a. 3/2 b. 3 c. 11/3 d. 2 (4) 54(10 + 20) = (54 x 10) + (54 x 20) is an example of a. Associative Property b. Distributive property c. Closure Property d. Commutative Property (5) A lighthouse has two lights-one that f lashes every 2 minutes, and another that f lashes every 1 1 2 minutes. Suppose the lights f lash together at noon. What is the f irst time af ter 1 pm that they will f lash together again? a. 1:03 b. 1:06 c. 1:01 d. 1:02
(6) Observe the f ollowing patterns. Find the sums of numbers f rom 141 to 150. ID : pk-6-natural-and-whole-numbers [2] 41+42+43+44+45+46+47+48+49+50=455 51+52+53+54+55+56+57+58+59+60=555 61+62+63+64+65+66+67+68+69+70=655 71+72+73+74+75+76+77+78+79+80=755 81+82+83+84+85+86+87+88+89+90=855 91+92+93+94+95+96+97+98+99+100=955 a. 1555 b. 1455 c. 1355 d. 2155 (7) If you write down all the numbers f rom 1 to 175 (including 1 and 175), how many digits would you have written down? a. 425 b. 417 c. 418 d. 411 (8) If a number is divisible by 10 and 6, it will be necessarily divisible by a. 30 b. 28 c. 35 d. 32 (9) In whole numbers, the associative property is satisf ied with the f ollowing operations a. Only Subtraction b. Division and Multiplication c. Addition and Multiplication d. Subtraction and Division (10) How many times does the digit 1 appear in numbers f rom 1 to 100? a. 21 b. 23 c. 20 d. 22 Fill in the blanks (11) Fill in the blanks with the correct number: A) 264 7 = 264 23-264 B) 876 11 = 876 29-876 C) 992 9 = 992 17-992 D) 848 16 = 848 24-848 E) 366 6 = 366 26-366 F) 239 21 = 239 22-239 (12) T wo tankers contain 1494 litres and 306 litres of petrol respectively. T he largest measuring container which can measure the petrol of either tanker exactly will have a capacity of litres. (13) Ulf at has two sheets of paper. One sheet is 442 inches wide and the other sheet is 130 inches wide. She wants to divide the sheets into strips of equal width that are as wide as possible without wasting any paper. She should cut the strips inches wide to avoid any wastage.
ID : pk-6-natural-and-whole-numbers [3] Check True/False (14) Between any two non consecutive whole numbers there is a whole number. True False (15) 0 is the smallest natural number. True False 2016 Edugain (www.edugain.com). All Rights Reserved Many more such worksheets can be generated at www.edugain.com
Answers ID : pk-6-natural-and-whole-numbers [4] (1) 420 m Since an electric pole is there at every 12 m, it will be present at distances which are multiples of 12. Similarly, a telegraph pole is there at every 140 m. It will thus be present at distances which are multiple of 140. Now the distance at which both types of poles will be present again, should be a multiple of both 12 and 140. Theref ore, we need to f ind the Least Common Multiple (LCM) of 12 and 140 in order to f ind such distance. LCM of 12 and 140 = 420 m. Step 5 Theref ore, both types of poles will be together again af ter a distance of 420 m. (2) c. 2 Total number of questions in the exam = 16 Since each correct answer gets 10 marks, the maximum possible marks in the exam = 16 10 = 160 marks. Since Ishaq attempted all the questions and got a total of 130 marks, the marks lost by him = 160-130 = 30 marks. Since he loses 5 marks f or each wrong answer and each correct answer otherwise could get him 10 marks, the marks lost f or each wrong answer = 10 + 5 = 15. Step 5 The number of questions Ishaq answered wrong = Total marks lost Marks lost f or each wrong answer = 30 15 = 2 Step 6 Hence, Ishaq got 2 answers wrong.
(3) b. 3 ID : pk-6-natural-and-whole-numbers [5] Please have a look at this article on how to f ind LCM of f ractions www.edugain.com/blog/2011/06/26/lcm-of -f ractions/ From this aritcle we know that, LCM (a/b, c/d) = LCM(a,c)/HCF(b,d) Theref ore, LCM (3/2, 1/3) = LCM(3, 1)/HCF(2, 3) LCM (3/2, 1/3) = 3/1 LCM (3/2, 1/3) = 3 (4) b. Distributive property Distributive property of multiplication means multiplication distributes over addition. Formally, 'a(b + c) = ab + ac' Thus, 54(10 + 20) = (54 x 10) + (54 x 20) is an example of distributive property.
(5) b. 1:06 ID : pk-6-natural-and-whole-numbers [6] The f irst light f lashes every 2 minutes and the other light f lashes every 1 1 2 minutes. Once the two lights f lash together, the amount of time af ter which the two lights will f lash together again is equal to the LCM of 2 minutes and 1 1 2 minutes. Bef ore we calculate the LCM of 2 minutes and 1 1 2 minutes, let us translate both time periods f rom minutes to seconds. Since 1 minute = 60 seconds, 2 minutes = 2 60 = 120 seconds, and 1 1 2 minutes = 3 2 60 = 90 seconds. Let us now calculate the LCM of 120 and 90. All prime f actors of 120: 2 120 2 is a factor of 120 2 60 2 is a factor of 60 2 30 2 is a factor of 30 3 15 3 is a factor of 15 5 5 5 is a factor of 5 1 Thus, 120 = 2 2 2 3 5. All prime f actors of 90: 2 90 2 is a factor of 90 3 45 3 is a factor of 45 3 15 3 is a factor of 15 5 5 5 is a factor of 5 1 Thus, 90 = 2 3 3 5. Step 5 The LCM of 120 and 90 = 2 3 3 5 2 2 = 360.
Step 6 ID : pk-6-natural-and-whole-numbers [7] 360 seconds in minutes = 360 60 minutes = 6 minutes. Step 7 Now, we know that the two lights f lash together every 6 minutes. We have been told that the two lights f lashes together at noon. This means, that times when they f lash together again are 12:6, 12:12, 12:18, 12:24,... 1:06,... Theref ore, the time af ter 1 PM that the two lights will f lash together again = 1:06 PM. (6) b. 1455 We need to f ind the sum of the ten numbers f rom 141 to 150. This sum = (10 100) + Sum of numbers f rom 41 to 50. Looking at the patterns given to us, we f ind that the sum of numbers f rom 41 to 50 = 455 This means, the required sum = (10 100) + 455 = 1455
(7) b. 417 ID : pk-6-natural-and-whole-numbers [8] We need to f ind the total number of digits in all numbers f rom 1 to 175. The range of numbers f rom 1 to 175 can be broken into numbers with 1, 2 and 3 digits respectively: 1-digit numbers: 1 to 9: A total of 9-1 + 1 = 9 numbers. Number of digits = 9 1 = 9 2-digit numbers: 10 to 99: A total of 99-10 + 1 = 90 numbers. Number of digits = 90 2 = 180 3-digit numbers: 100 to 175: A total of 175-100 + 1 numbers = 76 numbers. Number of digits = 76 3 = 228 Total number of digits = Number of digits f rom 1-digit numbers + Number of digits f rom 2- digit numbers + Number of digits f rom 3-digit numbers = 9 + 180 + 228 = 417 Thus, the number of digits we would have written if we wrote down all the numbers f rom 1 to 175 is 417. (8) a. 30 If a number is divisible by two dif f erent numbers, it is necessarily divisible by their L.C.M. L.C.M of 10 and 6 = 30. Thus, if a number is divisible by 10 and 6, it will be necessarily divisible by 30.
(9) c. Addition and Multiplication ID : pk-6-natural-and-whole-numbers [9] T he Associative Property states that if we are adding or multiplying three or more numbers, it does not matter where we put the parenthesis. It is applicable f or addition and multiplication. For example, 3 + (5 + 7) = (3 + 5) + 7, 3 (5 7) = (3 5) 7. Theref ore, we can say that, in whole numbers the associative property is satisf ied with Addition and Multiplication. (10) a. 21 The digit 1 appears 10 times as a unit digit f rom numbers 1 to 100. The digit 1 appears 10 times as a tens digit f rom numbers 10 to 19. The digit 1 appears 1 time as a hundreds digit in number 100. Thus, the total number of times 1 appears in numbers 1 to 100 = 10 + 10 + 1 = 21 (11) A) 16 264 7 can be written as: 264 7 = 264 (23-16) 264 7 = 264 23-264 16 Thus, the correct number is 16. B) 18 876 11 can be written as: 876 11 = 876 (29-18) 876 11 = 876 29-876 18 Thus, the correct number is 18.
C) 8 ID : pk-6-natural-and-whole-numbers [10] 992 9 can be written as: 992 9 = 992 (17-8) 992 9 = 992 17-992 8 Thus, the correct number is 8. D) 8 848 16 can be written as: 848 16 = 848 (24-8) 848 16 = 848 24-848 8 Thus, the correct number is 8. E) 20 366 6 can be written as: 366 6 = 366 (26-20) 366 6 = 366 26-366 20 Thus, the correct number is 20. F) 1 239 21 can be written as: 239 21 = 239 (22-1) 239 21 = 239 22-239 1 Thus, the correct number is 1.
(12) 18 ID : pk-6-natural-and-whole-numbers [11] The container which can measure petrol of both tanks, should be such that its volume in litres should f ully divide 1494 and 306. T heref ore, capacity of the largest measuring container which can measure the petrol of either tanker exactly is the HCF of 1494 and 306. Let us f ind all prime f actors of 1494: 2 1494 2 is a factor of 1494 3 747 3 is a factor of 747 3 249 3 is a factor of 249 83 83 83 is a factor of 83 1 1494 = 2 3 3 83 Let us now f ind all prime f actors of 306: 2 306 2 is a factor of 306 3 153 3 is a factor of 153 3 51 3 is a factor of 51 17 17 17 is a factor of 17 1 306 = 2 3 3 17 The HCF of 1494 and 306 is = 2 3 3 = 18 Step 5 T heref ore, the largest measuring container which can measure the petrol of either tanker exactly will have a capacity of 18 liters.
(13) 26 ID : pk-6-natural-and-whole-numbers [12] Let the width of strip be x inches Since no cloth should be wasted, 442 inches should be divisible by x inches Similarly, 130 inches should be divisible by x inches Also x has to be as large as possible, theref ore x should be HCF of 442 and 130 x = HCF(442, 130) = 26 inches (14) True Whole numbers are the numbers 0, 1, 2, 3... Between every two non consecutive whole numbers we can always f ind a whole number. For example, 2 is a whole number between the whole numbers 1 and 3. Theref ore, the answer is true. (15) False Natural numbers are the numbers used f or counting: 1, 2, 3... 0 is not a natural number. Theref ore, the answer is f alse.