Lesson 7, Topic 2
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# How To Find Equivalent Fractions

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To find an equivalent fraction with a larger numerator and denominator, simply multiply both the numerator and the denominator of the given fraction by the same number.

For example:

$$\frac {2}{3} = \frac {2}{3}\: \times \: \frac {3}{3}= \frac {6}{9}$$

That is, $$\frac {2}{3}$$is equivalent to $$\frac {6}{9}$$

### Example 1

Convert 2/9 into an equivalent fraction with the denominator 27.

Solution

Divide the second denominator by the first denominator to obtain the multiplier.

i.e. 27 ÷ 9 = 3

$$\frac {2}{9}= \frac {2 \: \times \: 3}{9 \: \times \: 3} = \frac {6}{27}$$

⇒ $$\frac {2}{9}= \frac {6}{27}$$

### Example 2

Find the missing part of these fractions:

Solution

You can use $$\frac {20}{50}$$ as your reference fraction because both its numerator and denominator are given.

That is, $$\frac {20}{50} = \frac {2}{5}$$ (i.e. divide by 10)

We can use the fraction to obtain the multipliers.

$$\frac {?}{10} = \frac {2 \: \times \: 2}{2 \: \times \: 5} = \frac {4}{10}$$

$$\frac {12}{?} = \frac {6 \: \times \: 2}{6 \: \times \: 5} = \frac {12}{30}$$

$$\frac {?}{80} = \frac {16 \: \times \: 2}{16 \: \times \: 5} = \frac {32}{80}$$

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