Adding, subtracting, multiplying and dividing can be applied to mixed number fractions. Each has its own method that helps make sure the numerator and denominator are treated correctly.

Part of

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.

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

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

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

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

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

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