More on Multiplying Fractions

Multiplying numbers where one or both numbers are fractions can be done without a calculator. Just because you are multiplying does not mean the answer is larger than the original number. As you complete questions in this section ask yourself, is the answer going to be larger or smaller than the number I start with?

Finding a fraction of a whole number

Example

Find three quarters of $12$.

$\displaystyle{\frac34}$ of $12$ can be written as $\displaystyle{\frac34 {\color{red}\times}\frac{12}{1}}$. So

\begin{align*} \color{red}{\frac34\times\frac{12}{1}}&\color{red}{=\frac{3\times 12}{4\times 1}}\\[1ex] &\color{red}{=\frac{36}{4}}\\[1ex] &\color{red}{=9} \end{align*}

There is more than one way to multiply a fraction by a whole number. The method here follows these steps:

1. Write the whole number as a fraction with denominator $1$ $\displaystyle{\left(\frac{12}{1}\right)}$.
2. Multiply the numerators.
3. Multiply the denominators.
4. Simplify (where possible).

Multiplying fractions

Example

Find $\displaystyle{\frac23}$ of $\displaystyle{\frac35}$.

\begin{align*} \frac23\text{ of }\frac35 &= \frac23\times\frac35\\[1ex] &=\frac{2\times 3}{3\times 5}\quad\genfrac..{0pt}{0}{\color{blue}{\longleftarrow\text{multiply numerators}}}{\color{red}{\longleftarrow\text{multiply denominators}}}\\[1ex] &=\frac{6}{15}\quad\longleftarrow\text{simplify where possible}\\[1ex] &=\frac25 \end{align*}

Try the following multiplications. Write your answer in the simplest form as either an integer or a fraction of the form a/b.

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