What you need to know

Things to remember:

  • To find the fraction of a number or amount of something, we divide by the denominator and then multiply by the numerator.

Let’s think about what fractions are. Imagine we have a block.

 

 

And we cut this block in half.

 

 

What did we do? We divided it into two pieces. So, to find \dfrac{1}{2} we divide by 4.

How about if we cut the block into quarters?

 

 

What did we do? We divided it into four pieces. So, to find \dfrac{1}{4} we divide by 4.

How about if we cut the block into fifths?

 

 

What did we do? We divided it into five pieces. So, to find \dfrac{1}{5} we divide by 5.

Notice how we just divide by the denominator when we are looking for a fraction amount of something and there is a 1 on top of the fraction.

What is \dfrac{1}{5} of 20?

\dfrac{1}{5} of 20 = 20\div5=4

What is \dfrac{1}{12} of 72?

\dfrac{1}{12} of 72 = 72\div12=6

But, how about if we want to find something like \frac{3}{5} of 20? We have previously seen how to multiply fractions and whole numbers, so we can actually write \dfrac{3}{5}.

\frac{3}{5}=3\times\frac{1}{5}

So really, this is asking us to find 3 lots of \dfrac{1}{5} of 20.

\dfrac{1}{5} of 20 = 20\div5=4

3\times4=12

\dfrac{3}{5} of 20 = 12

This gives us the two steps we need for finding fraction amounts.

What is \dfrac{6}{7} of 21?

Step 1: Divide the amount by the denominator.

21\div7=3

Step 2: Multiply the number in Step 1 by the numerator.

3\times6=18

\dfrac{6}{7} of 21 = 18

Example Questions

Question 1: What is \dfrac{5}{9} 63?

Answer

Step 1: Divide the amount by the denominator.

 

63\div9=7

 

Step 2: Multiply the number in Step 1 by the numerator.

 

7\times5=35

 

\dfrac{5}{9} of 63 = 35

Question 2: What is \dfrac{3}{11} 88?

Answer

Step 1: Divide the amount by the denominator.

 

88\div11=8

 

Step 2: Multiply the number in Step 1 by the numerator.

 

3\times8=24

 

\frac{3}{11} of 88 = 24