## What you need to know

Things to remember:

• The easiest way to compare fractions is for them to have the same denominator.

John and Jane have a bar of chocolate. John eats $\dfrac{2}{4}$ of the chocolate bar and Jane eats $\dfrac{3}{8}$ of the chocolate bar. Who ate the most?

Jane’s fraction looks bigger, but let’s look at it as a diagram.

Looking at the diagram, we can see that Jane is eating 3 pieces and John is eating 2, so Jane is eating more!… But wait, they aren’t the same size. We need to make them the same. We can’t make all of Jane’s pieces bigger, but we can make John’s smaller!

Now that they are the same size, we can count them fairly. John ate 4 pieces and Jane ate 3. John ate the most. But let’s look at John’s chocolate as fraction now. We turned $\dfrac{1}{2}$ into $\dfrac{4}{8}$.

John = $\dfrac{4}{8}$

Jane = $\dfrac{3}{8}$

We can now clearly see that John’s fraction is bigger. To compare fractions, we need to make the denominator the same!

Which fraction is biggest?

$\dfrac{2}{3}$           $\dfrac{5}{6}$           $\dfrac{9}{12}$

We do this in 3 Steps:

Step 1: Find the biggest denominator.

The biggest denominator here is 12.

Step 2: Make the other denominators into the number in Step 1.

Hint: Remember, we have to multiply the TOP of the fraction as well.

$$\frac{2}{3}=\frac{2\times4}{3\times4}=\frac{8}{12}$$

$$\frac{5}{6}=\frac{5\times2}{6\times2}=\frac{10}{12}$$

So, our fractions become:

$\dfrac{8}{12}$         $\dfrac{10}{12}$       $\dfrac{9}{12}$

And we can see that $\dfrac{5}{6}$ is the biggest.

## Example Questions

#### Question 1: Which fractions is biggest, $\dfrac{4}{5}$ or $\dfrac{7}{10}$?

Step 1: Find the biggest denominator.

The biggest denominator here is 10.

Step 2: Make the other denominators into the number in step 1.

Hint: Remember, we have to multiply the TOP of the fraction as well.

$$\frac{4}{5}=\frac{4\times2}{5\times2}=\frac{8}{10}$$

So, our fractions become:

$\dfrac{8}{10}$         $\dfrac{7}{10}$

And we can see that $\dfrac{4}{5}$ is the biggest.

#### Question 2: Which fractions is smallest, $\dfrac{1}{2}$,$\dfrac{3}{4}$, or $\dfrac{7}{8}$?

Step 1: Find the biggest denominator.

The biggest denominator here is 8.

Step 2: Make the other denominators into the number in Step 1.

Hint: Remember, we have to multiply the TOP of the fraction as well.

$$\frac{1}{2}=\frac{1\times4}{2\times4}=\frac{4}{8}$$

$$\frac{3}{4}=\frac{3\times2}{4\times2}=\frac{6}{8}$$

So, our fractions become:

$\dfrac{4}{8}$           $\dfrac{6}{8}$           $\dfrac{7}{8}$

And we can see that $\dfrac{1}{2}$ is the smallest.