Page 90 - ICSE Math 5

Division of a Fraction by Another Fraction

To divide a fraction by another fraction, multiply the first fraction by the reciprocal of the second
fraction (divisor). Reduce the fraction to its lowest terms, if possible.
3 9
Example 29: Divide by .
8 4

3 9 3 4 4 9
Solution: ÷ = × (We know that is reciprocal of .)
8 4 8 9 9 4
1 1
3  4 1  1 1
= = =
8  9 2  3 6
2 3
2 14
Example 30: Divide 3 by .
9 27

2 14 (3  9) + 2 14 29 14
Solution: 3 ÷ = ÷ = ÷
9 27 9 27 9 27
3
29 27 29  27
= × =
9 14 9  14
1
29  3 87 3
= = = 6
1  14 14 14
Properties of Division of Fractions

2 4 4 2
• Two fractions cannot be divided in any order. For example, ÷ ≠ ÷ .
3 5 5 3
1 2
5
2 ÷ = × = 2  5 = 1  5 5 4 2 4 3 4  3 = 2  3 = 6
2
4
= ; ÷ = × =
3 5 3 4 3  4 3  2 6 5 3 5 2 5  2 5  1 5
2 1
5 6 2 4 4 2
Since ≠ , therefore ÷ ≠ ÷ .
6 5 3 5 5 3 Mental Maths
• When a fraction is divided by itself, the quotient is always 1. Fill in the blanks.
1 1 3 8
6 6 6 7 6  7 1  1 (a) 8  = ____
3
For example, ÷ = × = = = 1.
7 7 7 6 7  6 1  1 7 7
1 1 (b) 9  = ____
9
5
• When a fraction is divided by 1, the quotient is the fraction (c) 0  = ____
itself. 6
2
15 15 1 15 1 15  1 15 (d) 7  1 = ____
For example, ÷ 1 = ÷ = × = = .
23 23 1 23 1 23  1 23
• When 0 is divided by a fraction, the quotient is always 0.
8 11
For example, 0 ÷ = 0 × = 0.
11 8
• A fraction cannot be divided by 0 as divisibility by 0 is not defined.
3
For example, ÷ 0 is not defined.
5

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