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 MathsNumerical skills
Watch this video to learn about dividing fractions.
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For dividing fractions, keep the first fraction as it is, change the divide sign to a multiply and flip the second fraction upside down.
One way to remember this is:
Keep it, change it, flip it
Calculate: \(\frac{3}{8} \div \frac{3}{4}\)
\(= \frac{3}{8} \times \frac{4}{3}\)
Now we use the same method as multiplying fractions:
\(= \frac{{3 \times 4}}{{8 \times 3}}\)
Remember to look out for common factors that can cancel 鈥 in this case we would divide top and bottom by 3 and 4.
\(= \frac{{1 \times 1}}{{2 \times 1}}\)
(if we hadn鈥檛 cancelled we would now have \(\frac{12}{24}\) at this stage)
\(= \frac{1}{2}\)
Now try the example question below.
Calculate: \(5\frac{1}{4} \div 1\frac{2}{5}\)
When dividing mixed numbers change into improper fractions first
\(= \frac{{21}}{4} \div \frac{7}{5}\)
\(= \frac{{21}}{4} \times \frac{5}{7}\)
Cancel the 21 and 7 by dividing them both by 7
\(= \frac{{3 \times 5}}{{4 \times 1}}\)
Multiply the numerators and multiply the denominators
\(= \frac{{15}}{4}\)
Change back into a mixed number
\(= 3\frac{3}{4}\)