FRACTIONS AND ITS OPERATIONS PAPER II. I. Write 2 equivalent fractions each. a. 2/7 = 2*5 = 10 ; 2*3 = 6 7*5 = 35 7*3 = 21

Transcription

1 FRACTIONS AND ITS OPERATIONS PAPER II I. Write 2 equivalent fractions each a. 2/7 = 2* = 10 ; 2*3 = 6 7* = 3 7*3 = 21 So 10 and 6 are the equivalent fractions 3 21 b. 13/ = 13*2 = 26 ; 13 *3 = 39 *2 = 10 *3 = 1 So 26 and 39 are the equivalent fractions 10 1 c. 4/9 = 4 * = 20 ; 4*6 = 24 9* = 4 9*6 = 4 So 20 and 24 are the equivalent fractions 4 4 II. Convert to mixed fractions a. 166/4 = 41 4 ) Ans =

2 b. 13/1 = 9 1) Ans = c. 89/12 = 7 12)89-84 Ans = 7 12 d. 43/3 = 11 3) Ans = III. Convert to proper fractions IV. a. 1 9/4 = 1*4 + 9 = 69 ; Ans = 69 4 b. 17 2/ = 17* +2 ; Ans = 87 c. 9 6/8 = 9*8+6 ; Ans = 78 8 Identify type of fractions (proper, improper or mixed) a. 9/34 = Improper b. 29/18 = Improper c. 17/7 = Improper

3 d. 1/3 = Proper e. 14/2 = Proper V. Reduce to lowest terms a. 7632/42 = = 244 = Ans = b. 61/63 = 3 61 = Ans = c. 36/28 = 36 = Ans = 73 7 VI. Compare fractions a. /3, 2/7 = *7 = 3 2*3 = 6 3>

4 Since 3 is greater, in the above equation the fraction in which is the NR(always check for NR) is greater Ans = > b. 6/1, 4/= * = 30 1*4 = 60 60>30 Since 60 is greater, in the above equation the fraction in which 4 is the NR(always check for NR) is greater Ans = 6 < 4 1 c. /9,12/7= *7 = 3 12*9 = > 3 Since 108 is greater, in the above equation the fraction in which 12 is the NR(always check for NR) is greater Ans = < VII. Fill in the blanks a. 48/6 48/6 = 1 ( no need to whole calculations since any fraction divided by its reciprocal is 1) b. /10 */10 = ¼

5 Working * = c. 3 8/3 +12/9 = 12/ /3 d. Multiplicative inverse of 8 3/2 = 2/19 Working 8*2 +3 = 19/2 e. Multiplicative inverse of a proper fraction is an improper fraction f. Reciprocal of 23/764 = 764/23 g. 237/6 1 = 237/6 h. 789/4 0 = Cannot be divided by 0 i. 3467/243 *0* 2 = 0 VIII. Small Word Problems a. Out of 24 mugs in shop, quarter of the mugs was white. How many mugs were not white? Solution : 6 24 *1 = 6 4 So 6 mugs were white So, 24 6 = 18 mugs were not white Ans = 18 mugs Important b. 3/ out of 7 chocolates melted. How many chocolates melted? Solution : 1 3 * 7 = 4 Important Ans = 4 chocolates melted c. Ram read 4/6 of a book containing 360 pages? How many pages are left unread? Solution : 60 4 * 360 = So Ram read 240 pages = 120 pages were left unread Ans = 120 pages Important

6 IX. Do as directed a. 24/6 +8/3 = Since DR s are not the same find the LCM 3 6, 3 2, 1 LCM = 3*2 = 6 24/6 remains the same since the DR is already 6 8*2 = 16 3 *2 = 6 2 So, = 40 = Ans = 20 3 Changing fraction to DR with 6 b. 2/42-1/42 = 2 1 = 10 = (Since DR s are the same) = 21 Ans = 21 c. 7/12 +11/9 = Find the LCM since DR s are not the same 3 12, 9 2 4, 3 2, 3 LCM = 3 *2*2*3 = 36 7*3 = 21 12*3 = 36 11*4 = 44 9*4 = 36

7 So, = Ans = 6 36 d. 1/9 + 8/12 = Since DR s are not same find LCM LCM = 36 (see previous sum for working) 1 *4 = 60 9 * 4 = 36 8 * 3 = * 3 = So, = 84 = 28 = 14 = Ans = 7 3 X. Simplify Addition and Subtraction a. 3 8/2-6/ = 3*2 + 8 = 14 So 14/2 * + 6 = 31 So 31/ (Find the LCM since DR s are not the same) 2 LCM of 2, = 10 14* = 70 2* = 10 31*2 = 62 *2 = 10 So, = 8 = = Ans = 4

8 b. 3 9/6 2 8/4 = 6*3 = 18+9 = 27 2*4 = = (Since DR s are not the same find LCM) , 4 3, 2 LCM = 2 *3*2 = *2 = 4 6*2 = *3 = 48 4 *3 = = 6 = Ans = ½ c. 6 ¾ + 8 9/2 +8 6/ = 6*4+3 = 27 So 27/4 8*2+ 9 = 2 So 2/2 8*+6 = 46 So 46/ (Since DR s are not the same find the LCM) , 2, 2 2, 1, 1 LCM = 2*2 = 4 27/4 remains the same since the DR is already 4 2*2 = 0 2 *2 = 4

9 46*2 = 92 2*2 = 4 So, = Ans = 109/4 d. 3 2/ + 8/ /3 = 3* +2 = 17 So 17/ *4 + 8 = 28 So 28/4 6*3 + 8 = 26 So 26/ (Since DR s are not the same find the LCM) 4 3 2, 4, 3, 2, 3 LCM = 2**2*3 = * 12 = 204 * *1 = 420 4* 1 = *20 = 20 3* 20 = So, = Ans = 72 3 e. 2 8/ + 3 6/8 = 2* +8 = 18 So 18/ 8*3 +6 = 30 So 30/8

10 LCM = * 8 = 144 * 8 = 40 30* = 10 8 * = So, = Ans = 147/4 f. 3 /9 +7/6 4 2/3 3*9 + = 32 So = 32/9 4*3 +2 = 14 So = 14/ , 6, 3 3, 2, 1 LCM = 3*3*2 = 18 32*2 = 64 9*2 = 18 7 *3 = 21 6*3 = *6 = 84 3*6 = 18 So, = Ans = 1 18

11 XI. Simplify Multiplication and Division a. 12/9 *6/3 = * 6 = Ans = 8/3 b. 1/8 7/64 * 12/ = 8 1 * 64 * 12 = Ans = 96/2 c. 200/600 /2= Ans = 2/ * 2 = XII. Word problems a. A hotel manager bought 2 ¼ kg of tomatoes, 3 ½ kg of onions and 1 ¾ kg of potatoes. How many kgs of vegetables did he buy in whole? Solution : Kgs of tomatoes the hotel manger bought = 2 ¼ 2*4 +1 = 9 So 9/4 Kgs of onions the hotel manger bought = 3 ½ 3*2 +1 = 7 So 7/2 Kgs of potatoes the hotel manger bought = 1 ¾ 1*4+3 = 7 So 7/4 So , 2, 2 2, 1, 1 LCM = 2*2 = 4

12 So 9/4 remains the same since the DR is 4 7*2 = 14 2 *2 = 4 So, = Ans = 37/4 kgs Important b. The product of two numbers is 4 2/7. If one number is 2, find the other number? Solution: The product of numbers = 4 2/7 4*7 +2 = 30 So 30/7 One number = 2 Other number = * Ans = 1/7 c. If an orphanage consumes 6 ¾ kgs of rice in a month. What is the consumption of 2 4/3 orphanages? Solution - No of kgs the orphanage consumes in a month = 6 ¾ 6*4 +3 = 27 So 27/4 So consumption of 24/3 orphanages in a month = 2 4 * *3+4 = 10 So 10/3 Conversion to mixed fraction 10 * 27 9 = 4 = 22 1 kgs Ans = 22 ½ kgs is the rice consumption

13 d. A shopkeeper had 42 kgs of sweets. 3/2 kg of sweets went bad. How many kgs went bad? How many kgs were good? Solution : No of kgs of sweets a shopkeeper had = 42 No of kgs of sweets that went bad = 3/2 No of kgs that were good = LCM of 2,1 = 2 42 *2 = * 2 = 2 Conversion to mixed fraction So, = 901 kgs = 4 1 kgs Ans = 4 ½ kgs were good ********************THE END*******************