Page 79 - ICSE Math 6

7. Write the following fractions in descending order.
7 6 13 2 11 9 7 5 13 7 9 11 13
(a) ,, (b) , , (c) , , (d) , , ,
9 5 18 7 14 28 9 12 36 10 40 20 30
Fundamental Operations on Fractions

Addition and subtraction of like fractions

To add or subtract like fractions, just add or subtract their numerators and keep the denominator the
same. Also, reduce the result to the lowest terms, if needed.
Example 17: Evaluate.

3 7 5 5 2 2
(a) + (b) 1+ (c) – (d) 1–
5 5 12 13 13 7
3 7 3 7+ 10 5 12 5 12 5+ 17
Solution: (a) + = = = 2 (b) 1+ = + = =
5 5 5 5 12 12 12 12 12

5 2 5 2− 3 2 7 2 7 2− 5
(c) – = = (d) 1– = − = =
13 13 13 13 7 7 7 7 7
Addition and subtraction of unlike fractions or mixed fractions

To add or subtract unlike fractions, we convert them into like fractions and then perform the respective
operation. For addition or subtraction of mixed fractions, we first convert them into improper fractions
and then perform addition or subtraction accordingly. Alternatively, we can add or subtract the whole
and fractional parts separately.

Example 18: Evaluate.
1 7 5 3 3
(a) 8 + + (b) 6 − 3
3 9 27 5 4

1 (8×3) 1+ 25
Solution: (a) As, 8 = =
3 3 3
1 7 5 25 7 5
\ 8 + + = + +
3 9 27 3 9 27
LCM of 3, 9, 27 = 27
1 25 25×9 225
\ 8 = = = (27 ÷ 3 = 9)
3 3 3×9 27
7 = 7×3 = 21 (27 ÷ 9 = 3)
9 9×3 27
5 5 × 1 5
27 = 27 × 1 = 27 (27 ÷ 27 = 1)
1 7 5 225 21 5 251 8
So, 8 + + = + + = = 9
3 9 27 27 27 27 27 27

3 (6×5) 3+ 33 3 (3×4) 3+ 15
(b) As, 6 = = and 3 = =
5 5 5 4 4 4
3 3 33 15
\ 6 – 3 = –
5 4 5 4

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