Adding and subtracting fractions

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}}