Page 32 - ICSE Math 7

Addition and subtraction

To add or subtract fractions, we have two cases:
(a) If the fractions to be added or subtracted are like fractions, then just add or subtract their numerators
since their denominators are the same.
(b) If the fractions to be added or subtracted are unlike fractions, then convert them into like fractions
and then perform addition or subtraction as explained above.
Alternatively,
Numerator of the first fraction × (LCM of denominators ÷ denominator
of the first fraction) + numerator of the second fraction × (LCM of
denominators ÷ denominator of the second fraction)
Sum =
LCM of denominators
This rule can be used for any number of fractions. For subtraction of fractions, replace ‘+’ with
‘–’ sign.
(c) If the fractions to be added or subtracted are mixed fractions, then convert all the mixed fractions
into improper fractions. After performing addition or subtraction on these fractions reduce the
result to its simplest form and if the result is an improper fraction, convert it to a mixed fraction.

Example 9: Simplify the following.
20 9 1 3 7
(a) – (b) 2 – 4 + 7
21 14 3 5 10
Solution: (a) LCM of 21 and 14 = 42

20 = 20 × 2 = 40 ( 42 ÷ 21 = 2)
21 21 × 2 42
9 = 9 × 3 = 27 ( 42 ÷ 14 = 3)
14 14 × 3 42

So, 20 – 9 = 40 – 27 = 13
21 14 42 42 42
1 2 × 3 + 1 7 Try These
(b) 2 = =
3 3 3 1. Find the value of x, if
3
3
x
4 = 4 × 5 + 3 = 23 1 + 2 = 3 17 .
20
5
4
5 5 5 2. What should be added to
5
7 7 = 7 × 10 + 7 = 77 to get ? 6
7
10 10 10 4
LCM of 3, 5 and 10 = 30
7 = 7 × 10 = 70
3 3 × 10 30
23 23 × 6 138
= =
5 5 × 6 30
77 = 77 × 3 = 231
10 10 × 3 30

1 3 7 7 23 77 70 138 231 163 13
So, 2 – 4 + 7 = – + = – + = = 5
3 5 10 3 5 10 30 30 30 30 30

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