 Hong Kong
Stage 2

# Equivalent Fractions

Lesson

In order to add or subtract fractions, you sometimes need to convert the fractions so that they have the same denominator (the bottom part of the fraction).

Equivalent fractions have the save value but could look different, here is another example of equivalent fractions you may already be used to. See here how

$1$1 half = $2$2 quarters = $4$4 eighths

$\frac{1}{2}$12 = $\frac{2}{4}$24 = $\frac{4}{8}$48

Now we don't want to have to make lots of paper fractions every time we do a fraction question, so we can use a numeric way of creating equivalent fractions.

For example, to add up $\frac{1}{20}$120 and $\frac{1}{10}$110, you would first have to convert $\frac{1}{10}$110 so that it has a common denominator of $20$20 with the other term you want to add. To do this, you would have to multiply both the top and bottom parts of $\frac{1}{10}$110 by $2$2, to get $\frac{2}{20}$220.

Remember:

The process for converting a fraction into an equivalent fraction is always the same:
multiply both top and bottom by the same number.

#### Worked Examples

##### Question 1

Fill in the blank to find an equivalent fraction to $\frac{7}{9}$79:

1. $\frac{7}{9}=\frac{\editable{}}{27}$79=27

##### Question 2

Fill in the blank to find an equivalent fraction to $\frac{8}{9}$89:

1. $\frac{8}{9}=\frac{40}{\editable{}}$89=40

##### Question 3

Fill in the blanks below to complete the equivalent fractions to $4\frac{2}{7}$427:

1. Mixed Number Improper Fraction Equivalent Fraction
$4\frac{2}{7}$427 $\frac{\editable{}}{7}$7 $\frac{180}{\editable{}}$180