Add and subtract factions with different denominators
\(\frac{1}{2} + \frac{1}{3} = ?\)
It is less straightforward to picture the answer to this addition because the denominators (bottom numbers) are different.
Rewriting the calculation using equivalent fractions with a common denominator (in this case, \({6}\)), makes it easier:
\(\frac{1}{2} + \frac{1}{3}\)
\(\frac{3}{6} + \frac{2}{6}\)
\(= \frac{5}{6}\)
You can use this method to add or subtract fractions:
- Multiply the two terms on the bottom to get the same denominator
- 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
- 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
- Now add/subtract the top numbers and keep the bottom number so that you now have one fraction
- Simplify the fraction if required
Use the information above to help with the example questions below:
Question
Calculate the following:
- \(\frac{2}{5} + \frac{3}{7}\)
- \(\frac{7}{8} + \frac{1}{9}\)
- \(\frac{9}{10} - \frac{1}{6}\)
- \(= \frac{{2 \times 7}}{{5 \times 7}} + \frac{{3 \times 5}}{{5 \times 7}}\)
- \(= \frac{{14}}{{35}} + \frac{{15}}{{35}}\)
- \(= \frac{{29}}{{35}}\)
- \(= \frac{7 \times 9}{8 \times 9} + \frac{1 \times 8}{8 \times 9}\)
- \(= \frac{63}{72} + \frac{8}{72}\)
- \(= \frac{71}{72}\)
- \(= \frac{9 \times 6}{10 \times 6} - \frac{1 \times 10}{10 \times 6}\)
- \(= \frac{54}{60} - \frac{10}{60}\)
- \(= \frac{44}{60} = \frac{11}{15}\)