When adding and subtracting fractions, we must ensure that we have the same denominator.

Step 1: Multiply the two terms on the bottom to get the same denominator:

Step 2: Multiply the top number on the first fraction with the bottom number of the second fraction to get the new top number of the first fraction:

Step 3: Multiply the top number on the second fraction with the bottom number of the first fraction to get the new top number of the second fraction:

Step 4: Now add/subtract the top numbers and keep the bottom number so that you now have one fraction:

Step 5: Simplify the fraction if required.

Use the information above the help with the example questions below.

Question

Calculate $$\frac{2}{5} + \frac{3}{7}$$

$= \frac{{2 \times 7}}{{5 \times 7}} + \frac{{3 \times 5}}{{5 \times 7}}$

$= \frac{{14}}{{35}} + \frac{{15}}{{35}}$

$= \frac{{29}}{{35}}$

There is also the possibility of sometimes using a common multiple.

Question

Calculate $$\frac{3}{4}+\frac{5}{6}$$

The denominators 4 and 6 have common multiple 12.

$$\frac{3}{4}$$ is equivalent to $$\frac{9}{12}$$

$$\frac{5}{6}$$ is equivalent to $$\frac{10}{12}$$

So $$\frac{3}{4}+\frac{5}{6}$$

$=\frac{9}{12}+\frac{10}{12}$

$=\frac{19}{12}$

$=1\frac{7}{12}$

Question

Calculate $$\frac{2}{3} - \frac{1}{6}$$

Method one

$= \frac{{2 \times 6}}{{3 \times 6}} - \frac{{1 \times 3}}{{3 \times 6}}$

$= \frac{{12}}{{18}} - \frac{3}{{18}}$

$= \frac{9}{{18}}$

$= \frac{1}{2}$

Method two

As the denominators 3 and 6 have common multiple 6 we can use this multiple as our new denominator.

Also $$\frac{2}{3}$$ is equivalent to $$\frac{4}{6}$$

So we get $$\frac{2}{3}-\frac{1}{6}$$

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

$=\frac{3}{6}$

$=\frac{1}{2}$

Question

Calculate $$2\frac{2}{5} + 3\frac{2}{3}$$

We add the whole number parts first $$(2+3=5)$$ and the add on the fractions.

$= 5 + (\frac{2}{5} + \frac{2}{3})$

$= 5 + (\frac{{2 \times 3}}{{5 \times 3}} + \frac{{2 \times 5}}{{5 \times 3}})$

$= 5 + (\frac{6}{{15}} + \frac{{10}}{{15}})$

$= 5 + (\frac{{16}}{{15}})$

$= 5 + (1\frac{1}{{15}})$

$= 6\frac{1}{{15}}$