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.

\[= 5 + (\frac{2}{5} + \frac{2}{3})\]

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

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

\[= 5 + (\frac{{16}}{{15}})\]

\[= 5 + (1\frac{1}{{15}})\]

\[= 6\frac{1}{{15}}\]