Resources for Multiplying and Dividing Fractions
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Questions
10
With Worked SolutionClick Here -
Video Tutorials
2
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Multiplying and Dividing Fractions Theory
![When multiplying fractions it is important to rearrange the fractions so that one or both can be changed to a simpler fraction. The numerators and denominators are then multiplied.\\ For mixed fractions, the mixed fraction is changed to an improper fraction where the numerator is greater than the denominator.\\ \textbf{Example 1}\\ Evaluate:\\ \textbf{i)} \(\dfrac{4}{10} \times \dfrac{6}{8}\)\\ \textbf{ii)} \(2 \dfrac{1}{2} \times 1 \dfrac{1}{4}\)\\ \textbf{Example 1 solution}\\[3pt] \textbf{i)} \(\begin{aligned}[t] \frac{4}{10} \times \frac{6}{8} & =\frac{2}{5} \times \frac{3}{4} \\ & =\frac{2 \times 3}{5 \times 4} \\ & =\frac{3 \times 2}{5 \times 4} \\ & =\frac{3}{5} \times \frac{1}{2} \\ & =\frac{3}{10} \end{aligned}\)\\[3pt] \textbf{ii)} \(\begin{aligned}[t] 2 \frac{1}{2} \times 1\frac{1}{4} & =\left(\frac{4}{2}+\frac{1}{2}\right) \times\left(\frac{4}{4}+\frac{1}{4}\right) \\ & =\frac{5}{2} \times \frac{5}{4} \\ & =\frac{25}{8} \\ & =\frac{24+1}{8} \\ & =\frac{24}{8}+\frac{1}{8} \\ & =3 \frac{1}{8} \end{aligned}\) \columnbreak When dividing fractions the fraction on the right is inverted and then the fractions are multiplied.\\ \textbf{Example 2}\\ Evaluate\\ \textbf{i)} \(\dfrac{4}{9} \div \dfrac{2}{3}\)\\ \textbf{ii)} \(3 \dfrac{1}{3} \div \dfrac{5}{9}\)\\ \textbf{Example 2 solution}\\[3pt] \textbf{i)} \(\begin{aligned}[t] \frac{4}{9} \div \frac{2}{3} & =\frac{4}{9} \times \frac{3}{2} \\ & =\frac{3}{9} \times \frac{4}{2} \\ & =\frac{1}{3} \times \frac{2}{1} \\ & =\frac{2}{3} \end{aligned}\)\\ \textbf{ii)} \(\begin{aligned}[t] 3 \frac{1}{3} \div \frac{5}{9} & =\left(\frac{9}{3}+\frac{1}{3}\right) \times \frac{9}{5} \\ & =\frac{10}{3} \times \frac{9}{5} \\ & =\frac{10}{5} \times \frac{9}{3} \\ & =\frac{2}{1} \times \frac{3}{1} \\ & =6 \end{aligned}\) \end{multicols}](/media/qgsoeibj/7929.png)