# Comparing fractions

It is important that your
child can compare different fractions and determine which is larger,
which is smaller, or if they are equal.

Discuss with your children how, with a fraction, when the bottom number (denominator) increases, the fraction gets smaller. Explore this with them using real examples (chocolate bars and pizza are popular!).

Review the three different comparison
situations below. Note: This fraction
number line will help with comparing
fractions.

## Same numerator, Different denominator

In this case there are the same number of different things.
In this case the things are thirds and sixths. Ensure your child that
understands
that thirds are larger than sixths. The rule
for comparing here is that the fraction with the smaller denominator
is the
largest

## Different numerator, Same denominator

Here we have a different number of the same thing – there are
seven eighths and three eighths. Seven is a larger number than three.
The
comparison rule here is that the fraction with the greatest numerator
is the largest.

## Different numerator, Different denominator

This is a more difficult task the two comparisons above. Depending
on your child’s level, this maybe a step you skip and then come
back to later.

These fractions are compared by changing the denominators to a common
number. This can be done by multiplying the top and bottom of the fraction
by the same number since this will give a fraction with an equivalent
value. Do this as shown below to both fractions to get a common denominator
and then compare them.

So, in the example above, now that the denominators are equal, the fraction with the greatest numerator is the largest.

Some students may respond to questions about which fraction is bigger by saying it depends on what size the whole is and, depending on the wording of the question, they may actually be correct! Encourage them to think in terms which is the larger or smaller share and be precise with your questions. e.g. *"which is the largest ***fraction**?" not just "*which is the largest*?"

## Worksheets

Practice comparing fractions with the worksheets above.