Multiplying and Dividing Fractions: Practice

The word 'of' means multiply, and $20 = \frac{20}{1}$.

$\frac{3}{4} \times 20 = \frac{3 \times 20}{4} = \frac{60}{4} = 15$

A quick check: $\frac{1}{4}$ of $20$ is $5$, and three quarters is $3 \times 5 = 15$.

To undo a multiplication by $\frac{2}{3}$, divide by $\frac{2}{3}$, which means multiplying by $\frac{3}{2}$.

$? = \frac{1}{2} \div \frac{2}{3} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4}$

Check: $\frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}$.

Work from the inside out. First $\frac{2}{3}$ of $12$:

$\frac{2}{3} \times 12 = \frac{2 \times 12}{3} = 8$

Then take half of that result:

$\frac{1}{2} \times 8 = 4$

Write $4 = \frac{4}{1}$ and multiply by the reciprocal of $\frac{2}{3}$.

$4 \div \frac{2}{3} = \frac{4}{1} \times \frac{3}{2} = \frac{12}{2} = 6$

Multiplying by $\frac{2}{3}$ instead would give $\frac{8}{3}$, which is wrong.

The word 'of' means multiply, and $35 = \frac{35}{1}$.

$\frac{2}{5} \times 35 = \frac{2 \times 35}{5} = \frac{70}{5} = 14$

A quick check: $\frac{1}{5}$ of $35$ is $7$, and two fifths is $2 \times 7 = 14$.

Write $4 = \frac{4}{1}$ and multiply straight across.

$\frac{3}{8} \times \frac{4}{1} = \frac{3 \times 4}{8 \times 1} = \frac{12}{8} = \frac{3}{2}$

The last step divides top and bottom by $4$. Multiplying $4$ into the denominator would give $\frac{3}{32}$, which is wrong.

The divisor is what you divide the first fraction by, so divide $\frac{5}{6}$ by the result $\frac{5}{12}$.

$? = \frac{5}{6} \div \frac{5}{12} = \frac{5}{6} \times \frac{12}{5} = \frac{60}{30} = 2$

Check: $\frac{5}{6} \div 2 = \frac{5}{6} \times \frac{1}{2} = \frac{5}{12}$.

The word 'of' means multiply, and $16 = \frac{16}{1}$.

$\frac{3}{4} \times 16 = \frac{3 \times 16}{4} = \frac{48}{4} = 12$

A quick check: $\frac{1}{4}$ of $16$ is $4$, and three quarters is $3 \times 4 = 12$.

Write $10 = \frac{10}{1}$ and multiply by the reciprocal of $\frac{2}{5}$.

$10 \div \frac{2}{5} = \frac{10}{1} \times \frac{5}{2} = \frac{50}{2} = 25$

Multiplying by $\frac{2}{5}$ instead would give $4$, which is wrong.

The word 'of' means multiply, and $24 = \frac{24}{1}$.

$\frac{5}{8} \times 24 = \frac{5 \times 24}{8} = \frac{120}{8} = 15$

A quick check: $\frac{1}{8}$ of $24$ is $3$, and five eighths is $5 \times 3 = 15$.

Write $9 = \frac{9}{1}$ and multiply by the reciprocal of $\frac{3}{4}$.

$9 \div \frac{3}{4} = \frac{9}{1} \times \frac{4}{3} = \frac{36}{3} = 12$

Multiplying by $\frac{3}{4}$ instead would give $\frac{27}{4}$, which is wrong.

Dividing by $\frac{1}{2}$ is the same as multiplying by $2$, so the unknown doubles to give $6$. Undo it by halving.

$? = 6 \times \frac{1}{2} = 3$

Check: $3 \div \frac{1}{2} = 3 \times 2 = 6$.