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

Question 1:  Write \dfrac{25}{4} as a mixed number.

Answer

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}

Question 2: Write \dfrac{113}{12} as a mixed number.

Answer

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}