Page 148 - Start Up Mathematics_6

5 1
(c) –
6 3
LCM of 6 and 3 = 6
5 1 5 1 2 5 2 5 – 2 3 1
∴ – = – × = – = = =
6 3 6 3 2 6 6 6 6 2

2 3 1
(d) + –
3 4 2
LCM of 3, 4 and 2 = 12

We convert the given fractions into equivalent fractions with denominator 12.
2 = 2 × 4 = 8 3 3 × 3 = 9 1 1 × 6 = 6
; =
; =
3 3 × 4 12 4 4 × 3 12 2 2 × 6 12
2 3 1 8 9 6 8 + 9 – 6 11
Now + – = + – = =
3 4 2 12 12 12 12 12

Case 3: Addition and subtraction of mixed fractions
To add or subtract mixed fractions, we first convert each mixed fraction into improper fraction
and proceed as in Case 2.
OR

Add or subtract whole and fractional parts separately.
2 1
Example 35: Solve 4 + 3
3 4
2 1 4 × 3 + 2 3 × 4 + 1 14 13
Solution: 4 + 3 = + = +
3 4 3 4 3 4
14 × 4 13 × 3 56 39
= + = + ( LCM of 3 and 4 is 12)
3 × 4 4 × 3 12 12

95 11
= = 7
12 12
Aliter:
2 1 2 1  2 1
4 + 3 = 4 + + 3 + = (4 + 3) +  + 
3 4 3 4  3 4 
 2 1  2 4 1 3
= 7 +  +  =+ × + × 
7 
 3 4   3 4 4 3 
 8 3  11 11
7
= 7 +  +  =+ = 7 ( LCM of 3 and 4 is 12)
 12 12  12 12
2 3
Example 36: Sarita bought m of ribbon and Lalita bought m of ribbon. What is the total
5 4
length of the ribbon they bought? (NCERT)
2
Solution: Sarita bought m of ribbon.
5

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