Page 77 - ICSE Math 5

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For example, let’s find three equivalent fractions of by dividing.
16
8 8 ÷ 2 4 8 8 ÷ 4 2 8 8 ÷ 8 1
4 16
16 = 16 ÷ 2 = ; = 16 ÷ 4 = ; = 16 ÷ 8 = 2
8 16
4 2 1 8
So, , and are the equivalent fractions of .
8 4 2 16
8 4 2 1
This can also be written as = = = .
16 8 4 2
1
Example 1: Find three equivalent fractions of .
7
1 1 × 2 2 1 1 × 3 3 1 1 × 4 4
Solution: = = ; = = ; = =
7 7 × 2 14 7 7 × 3 21 7 7 × 4 28

1 2 3 4 1 2 3 4
So, the equivalent fractions of are , and , i.e., = = = .
7 14 21 28 7 14 21 28
Example 2: Fill in the boxes.
2 63 7
(a) = (b) =
5 10 81
2 63 7
Solution: (a) = (b) =
5 10 81
5 × ? = 10 63  ? = 7
We know that 5 × 2 = 10. Since 63  9 = 7,
Thus, the numerator 2 should the denominator 81 should

also be multiplied by 2. also be divided by 9.
2 2 × 2 4 63 63  9 7
So, = = . So, = = .
5 5 × 2 10 81 81  9 9
To check whether the given fractions are equivalent or not, we cross-multiply, i.e., multiply the
numerator of the first fraction with the denominator of the second fraction and the denominator
of the first fraction with the numerator of the second fraction. If the products obtained are equal,
then we say that the fractions are equivalent, otherwise not.
1 4
Example 3: Check whether and are equivalent fractions or not.
3 12
1 4
Solution: =
3 12
On cross-multiplication, we get 1 × 12 = 4 × 3, i.e., 12 = 12.
1 4
Since the products are equal, and are equivalent fractions.
3 12
2 7
Example 4: Check whether and are equivalent fractions or not.
7 9
2 7
Solution: =
7 9
On cross-multiplication, we get 2 × 9  7 × 7, i.e.,
18  49.
2 7
Since the products are not equal, and are not equivalent fractions.
7 9
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