 # Mixed questions on fractions (comparing, equivalence, simplifying and ordering)

Lesson

You may have learned about equivalent fractions, comparing fractions, ordering fractions and simplifying fractions. This chapter will revisit each of these concepts.

## Comparing fractions

When we compare fractions, we look at which one is larger and which one is smaller. Sometimes it can be hard to do this just by looking, so it may help to compare an equal number of parts. Watch this video to revisit comparing fractions.

Now try this question for yourself.

##### Question 1

Let's compare the fractions $\frac{1}{2}$12 and $\frac{1}{3}$13.

1. Fill the box below to change $\frac{1}{2}$12 into sixths.

$\frac{1}{2}=\frac{\editable{}}{6}$12=6

2. Fill the box below to change $\frac{1}{3}$13 into sixths.

$\frac{1}{3}=\frac{\editable{}}{6}$13=6

3. Fill in the boxes to make the statement true.

$\frac{1}{2}$12 is the same as $\frac{\editable{}}{6}$6 and $\frac{1}{3}$13 is the same as $\frac{\editable{}}{6}$6.

4. Which fraction is larger?

$\frac{1}{3}$13

A

$\frac{1}{2}$12

B

## Ordering fractions

We may need to put a group of fractions into ascending order (smallest to largest) or descending order (largest to smallest). Watch this video to revisit ordering fractions.

Now try this question for yourself.

#### Worked example

##### Question 2

Arrange the following fractions in descending order: $\frac{9}{10}$910, $\frac{2}{5}$25, $\frac{4}{7}$47

## Equivalent fractions

Equivalent fractions are different ways of representing the same value. We can use equivalent fractions when we compare or order fractions. Watch this video to revisit equivalent fractions.

Now try this question for yourself.

#### Worked example

##### Question 3

Fill in the blank to find an equivalent fraction to $\frac{7}{4}$74:

1. $\frac{7}{4}=\frac{\editable{}}{24}$74=24

## Simplifying fractions

Simplifying a fraction means we divide the numerator and the denominator by the highest common factor. Watch this video to revisit simplifying fractions.

Now try this question for yourself.

#### Worked example

##### Question 4

Express the following fraction in its simplest form: $\frac{20}{35}$2035

### Outcomes

#### NA4-4

Apply simple linear proportions, including ordering fractions