Adding and subtracting fractions
Watch this video to learn about 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.
\(= 5 + (\frac{2}{5} + \frac{2}{3})\)
\(= 5 + (\frac{{2 \times 3}}{{5 \times 3}} + \frac{{2 \times 5}}{{5 \times 3}})\)
\(= 5 + (\frac{6}{{15}} + \frac{{10}}{{15}})\)
\(= 5 + (\frac{{16}}{{15}})\)
\(= 5 + (1\frac{1}{{15}})\)
\(= 6\frac{1}{{15}}\)