Convert top-heavy fractions to mixed numbers | Year 5 Maths

## What you need to know

Things to remember:

• Complete the division and find the whole number answer with a remainder
• Use this to write down the mixed number

Let’s look at what a top-heavy fraction is:

$$\frac{20}{6}$$

This fraction is saying that we are cutting something into sixths, and we want 20 of them. As a picture, our fraction would look like this

Drawing it likes this tells us that we have 3 wholes and $\dfrac{2}{6}$, or $3\dfrac{2}{6}$ as a mixed number.

But how can we do convert it in a more ‘mathy’ way? Well, what is a fraction? What does it mean? Remember, a fraction is just a division question.

$$\frac{20}{6}=20\div6$$

Let’s do this division and see what we get.

$$\frac{20}{6}=20\div6=3\text{ remainder }2$$

So, doing this division gives us 3 whole pieces and 2 left over that still need to be divided by 6.

$$3\text{ remainder }2=3+2\div6$$

But, we can write the division as a fraction.

$$3+2\div6=3+\frac{2}{6}=3\frac{2}{6}$$

Like we had before! So, we did this in 3 steps.

Write $\dfrac{49}{9}$ as a mixed number.

Step 1: Do the division to find the whole number and the remainder.

$$\dfrac{49}{9}=49\div9=5\text{ remainder }4$$

Whole = 5

Remained = 4

Step 2: Put the remainder over the fraction.

$$\frac{4}{9}$$

Step 3: Put the whole number from Step 1 and the fraction from Step 2 together.

$$\frac{49}{9}=5\frac{4}{9}$$

## Example Questions

Step 1: Do the division to find the whole number and the remainder.

$$\frac{25}{4}=25\div4=6\text{ remainder }1$$

Whole = 6

Remained = 1

Step 2: Put the remainder over the fraction.

$$\frac{1}{4}$$

Step 3: Put the whole number from Step 1 and the fraction from Step 2 together.

$$\frac{25}{4}=6\frac{1}{4}$$

Step 1: Do the division to find the whole number and the remainder.

$$\frac{113}{12}=113\div12=9\text{ remainder }5$$

Whole = 9

Remained = 5

Step 2: Put the remainder over the fraction.

$$\frac{5}{12}$$

Step 3: Put the whole number from Step 1 and the fraction from Step 2 together.

$$\frac{113}{12}=9\frac{5}{12}$$