 What you need to know

Things to remember:

• See what to multiply the smaller denominator by.
• Multiply the top and bottom of the fraction to make the denominators the same.
• Add or subtract the fractions.

This topic will teach you how to add and subtract fractions where one denominator is a multiple of the other, like this:

$$\frac{3}{4} + \frac{1}{8}$$

To add and subtract fractions the denominators have to be the same. Are they the same here? No! So, we need to change one of them. Luckily for us, in this topic, one denominator will be a multiple of the other. Here, we can see that 8 is a multiple of 4:

$$4\times2=8$$

So, we can turn $\frac{3}{4}$ into a fraction with 8 on the bottom by multiplying the top and bottom by 2. Now that the denominators are the same, we can add them!

$$\frac{3}{4} + \frac{1}{8} = \frac{6}{8}+\frac{1}{8}=\frac{7}{8}$$

So, we did this in 3 Steps.

Complete the following subtraction

$$\frac{2}{5}-\frac{2}{15}$$

Step 1: Find the multiple, to see which fraction we change.

$$5\times3=15$$

15 is a multiple of 5, so we need to change the fraction with 5 on the bottom.

Step 2: Multiply the top and bottom of the fraction by the same number to make the denominators the same. Step 3: Add or subtract the fractions.

$$\frac{2}{5} - \frac{2}{15} = \frac{6}{15}-\frac{2}{15}=\frac{4}{15}$$

Example Questions

$$\frac{2}{5} - \frac{2}{15} = \frac{6}{15}-\frac{2}{15}=\frac{4}{15}$$

Step 1: Find the multiple, to see which fraction we change.

$$3\times4=12$$

12 is a multiple of 4, so we need to change the fraction with 4 on the bottom.

Step 2: Multiply the top and bottom of the fraction by the same number to make the denominators the same. Step 3: Add or subtract the fractions.

$$\frac{1}{3} + \frac{5}{12} = \frac{4}{12}+\frac{5}{12}=\frac{9}{12}$$