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EqUivALEnt FrACtionS

Fractions that represent the same part of a whole are called equivalent or equal
fractions.

Look at the following figures. The shaded parts of all the figures are equal.

1 2 3 4
2 4 6 8

1 2 3 4 1 2 3 4
Here, = = = . Thus, , , and are all equivalent fractions.
2 4 6 8 2 4 6 8

Finding Equivalent Fractions

• We can find equivalent fractions by multiplying the numerator and denominator
by the same non-zero number.

2
Example 1. Find three equivalent fractions of .
3

2 22 4 2 23 6 2 24 8
×
×
×
Solution. We have: = = ; = = ; = =
×
×
×
3 32 6 3 33 9 3 34 12
4 6 8 2
Hence, , and are three equivalent fractions of .
6 9 12 3
• We can also find equivalent fractions by dividing the numerator and denominator
by the same non-zero number.

8
Example 2. Find two equivalent fractions of .
12
8 8 ÷ 2 4 8 8 ÷ 4 2
Solution. We have: = = and = =
12 12 ÷ 2 6 12 12 ÷ 4 3
4 2 8
Hence, and are equivalent fractions of .
6 3 12

Checking for Equivalence

To check if two given fractions are equivalent or not, multiply the numerator of one
fraction with the denominator of the other. If the products are the same, then the

fractions are equivalent. Such multiplication is called cross-multiplication.

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Fractions