How To Find Equivalent Fractions

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:

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

Worked Example 7.2.1:

Convert \(\frac{2}{9}\) 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 

⇒ \( \frac {2}{9}= \frac {6}{27} \)

Worked Example 7.2.2:

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.

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

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

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