Fractions

NZ Level 3

Comparisons using equivalent fractions

Lesson

You may have already learned about comparing fractions using area models.

Now we will look at using equivalent fractions to compare the value of fractions.

Equivalent fractions are fractions that look different, but have the same value. Such as, $\frac{1}{2}$12 and $\frac{2}{4}$24

As you can see in the diagrams, they have the same value, but look different.

$\frac{1}{2}$12 and $\frac{2}{4}$24

Equivalent fractions are useful to be sure of the value compared to other fractions, so we can work out which fraction is bigger or smaller.

Watch this video to look at comparing fractions using equivalent fractions.

To compare fractions we need to think of their number family to help change them into an equal number of pieces. A number family is three numbers that fit together to make facts using multiplication, for example, $5$5, $2$2 and $10$10 because $5\times2=10$5×2=10.

Using this fact, we can make:

- fifths into tenths

by splitting each fifth into two equal parts

or

- halves into tenths

by splitting each half into five equal parts.

Remember!

When changing to an equivalent fraction we do not change the value of the fraction.

To change into an equivalent fraction we use number families to relate the denominators.

We are going to compare the two fractions $\frac{1}{8}$18 and $\frac{1}{4}$14.

Turn $\frac{1}{4}$14 into a fraction in eighths.

We can now compare the two fractions $\frac{1}{8}$18 and $\frac{1}{4}$14.

Which fraction is larger?

The fractions are the same size.

A$\frac{1}{8}$18

B$\frac{1}{4}$14

CThe fractions are the same size.

A$\frac{1}{8}$18

B$\frac{1}{4}$14

C

We are going to compare the two fractions $\frac{4}{6}$46 and $\frac{1}{3}$13.

Turn $\frac{1}{3}$13 into a fraction in sixths.

Now plot $\frac{4}{6}$46 and $\frac{1}{3}$13 on the numberline:

Which fraction is larger?

$\frac{1}{3}$13

A$\frac{4}{6}$46

B$\frac{1}{3}$13

A$\frac{4}{6}$46

B

We are going to compare the two fractions $\frac{40}{100}$40100 and $\frac{2}{5}$25.

Turn $\frac{2}{5}$25 into a fraction in hundredths.

Now compare $\frac{40}{100}$40100 and $\frac{2}{5}$25

$\frac{40}{100}=\frac{2}{5}$40100=25

A$\frac{40}{100}>\frac{2}{5}$40100>25

B$\frac{40}{100}<\frac{2}{5}$40100<25

C$\frac{40}{100}=\frac{2}{5}$40100=25

A$\frac{40}{100}>\frac{2}{5}$40100>25

B$\frac{40}{100}<\frac{2}{5}$40100<25

C

Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.