Page 108 - Start Up Mathematics_4

Equivalent Fractions

We can represent the same fraction in
different ways. Observe carefully how 1 2 3 4
each of these represent half of a circle. 2 4 6 8
Fractions that have the same value or represent the same
part of a whole are called equivalent fractions. →
1
Example 1: Cut a pie into pieces to represent in two
different ways. 2
1 of the pie
Solution: If a pie is cut into 2 pieces, each piece is 1 2
2
of the pie.

→
If a pie is cut into 4 pieces, then 2 pieces
represent the same amount of the pie that 2 1
1 did. 4 which is same as 2
2

We can get equivalent fractions of the given fraction by multiplying or dividing its numerator
and denominator by the same number.
2
Example 2: Find four fractions equivalent to by multiplying.
3
2 2 × 2 4 2 2 × 3 6 2 2 × 4 8 2 2 × 5 10
Solution: = = ; = = ; = = ; = =
3 3 × 2 6 3 3 × 3 9 3 3 × 4 12 3 3 × 5 15

2 4 6 8 10 Quick Tip
Thus, , , , and are equivalent
3 6 9 12 15
fractions. It is similar to finding
multiples of a number.

14
Example 3: Find two fractions equivalent to by
dividing. 28 Quick Tip

14 14 ÷ 7 2 14 14 ÷ 2 7 It is similar to finding
Solution: = = = =
28 28 ÷ 7 4 28 28 ÷ 2 14 factors of a number.

2 7 14
Thus, , and are equivalent fractions.
4 14 28
Example 4: Find equivalent fractions for the given fractions.

4 3 12 54
(a) = (b) = (c) =
9 45 5 63 7

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