Page 78 - classs 6 a_Neat

ADDITION OF FRACTIONS
EXAMPLE 4. Find the sum 7 + 11 + 9
ADDITION OF LIKE FRACTIONS 12 16 24
(Sum of their numerators) SOLUTION: LCM of 12, 16, 24 = ( 4 × 3 × 2 × 2) = 48.
RULE Sum of like fractions =
(Common denominator) 7 11 9 28 + 33 +18 [ 48 ÷ 12 = 4, 4 × 7 = 28] and

EXAMPLE 1. Find the sum: 12 + 16 + 24 = 48 { [ 48 ÷ 16 = 3, 3 × 11 = 33] }
4 2 3 1 5 [ 48 ÷ 24 = 2, 2 × 9 = 18]
(i) + (ii) + + = 79 =1 31
9 9 8 8 8 48 48
SOLUTION: We have:
4 2 (4 + 2) 6 2 2 5 7 11
(i) + = = = EXAMPLE 5. find the sum + +
9 9 9 9 3 6 8 12
3
3 1 5 (3 + 2 + 5) 9 1 SOLUTION: we have,
(ii) + + = = = 1
8 8 8 8 8 8 LCM of 6, 8,1 2 = (2 × 3 × 2 × 2) = 24.
ADDITION OF UNLIKE FRACTIONS
5 + 7 + 11 = 20 + 21 + 22 [ 24 ÷ 6 = 4, 4 × 5 = 20] and

RULE Change the givenfractions into equivalent like fractions and then add. 6 8 12 24 { [ 24 ÷ 8 = 3, 3 × 7 = 21] }
63 21 21 5 [ 48 ÷ 24 = 2, 2 × 11 = 22]
= = =2
8 5 24 8 8
EXAMPLE 2. Find the sum: + 8
9 12

SOLUTION: LCM of 9 and 12 = (3 × 3 × 4) = 36.
EXAMPLE 6. Find the sum: 2 4 +1 3 +3 1
Now, 8 + 8 × 5 = 32 and 5 = 5 × 3 = 15 . 5 10 15
9 9 × 4 36 12 12 × 3 36 SOLUTION: LCM of 5, 10, 15 = (5 × 2 × 3) = 30.
8 + 5 = 32 + 15 = (32 + 15) = 47 = 1 11 . 2 4 +1 3 +3 1 [ 30 ÷ 5 = 6, 6 × 14 = 84] ,

9 12 36 36 36 36 36 5 10 15 { [ 30 ÷ 10 = 3, 3 × 13 = 39] }
14 13 46 [ 30 ÷ 15 = 2, 2 × 46 = 92]
Short Method LCM of 9 and 12 = (3 × 3 × 4) = 36. = + +
5 10 15
84 + 39 + 92
84 + 39 + 92 215 43 43 1
8 + 5 = 32 + 5 { [ 36 ÷ 9 = 4, 4 × 8 = 32] and } = = 30 + 30 = 6 = 7 6
30
9 12 36 [ 36 ÷ 12 = 3, 3 × 5 = 15] 6

47 11 EXAMPLE 7. Tanvi bought a notebookjor ₹ 84 and a penjor ₹ 105• How much money should
= =1
36 36 she pay to the shopkeeper?
SOLUTION 3 35

5 3 Cost of a notebook ₹ 8 = ₹
EXAMPLE 3: Find the sum: + . 4 4
6 18 2 52
SOLUTION: LCM of 6 and 8 = (2 × 3 × 4 )= 24. Cost of a pen ₹ 10 5 = ₹ 5

5 + 3 = 20 + 9 { [ 24 ÷ 6 = 4, 4 × 5 = 20] and } ( 35 52 ) ( 175 + 208 )
6 8 24 [ 24 ÷ 8 = 3, 3 × 3 = 9] Total cost of both the articles= ₹ 4 + 5 = ₹ 20
= ₹ 383 = ₹19 3
29 5 20 20
= =1
24 24 3
Hence, Tanvi should pay ₹19 to the shopkeeper.
20