Multiplying and Dividing Fractions: Additional Practice (Set 2)

Write $6 = \frac{6}{1}$ and multiply by the reciprocal of $\frac{1}{2}$.

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

There are twelve halves in $6$. Multiplying by $\frac{1}{2}$ instead would give $3$, which is wrong.

This asks how many $\frac{1}{8}$ fit into $\frac{7}{8}$, which is $\frac{7}{8} \div \frac{1}{8}$. Multiply by the reciprocal.

$\frac{7}{8} \div \frac{1}{8} = \frac{7}{8} \times \frac{8}{1} = \frac{56}{8} = 7$

Seven eighths holds seven of the one-eighth pieces, so you get $7$ pieces.

This asks how many $\frac{3}{4}$ fit into $6$, which is $6 \div \frac{3}{4}$. Multiply by the reciprocal.

$\frac{6}{1} \times \frac{4}{3} = \frac{24}{3} = 8$

So there are $8$ servings. Multiplying by $\frac{3}{4}$ instead would give $\frac{9}{2}$, which is wrong.

The word 'of' means multiply, and $42 = \frac{42}{1}$.

$\frac{5}{6} \times 42 = \frac{5 \times 42}{6} = \frac{210}{6} = 35$

A quick check: $\frac{1}{6}$ of $42$ is $7$, and five sixths is $5 \times 7 = 35$.

Multiply the numerators together and the denominators together.

$\frac{2}{3} \times \frac{2}{3} = \frac{2 \times 2}{3 \times 3} = \frac{4}{9}$

Multiplying only the numerators and forgetting the denominators would give $\frac{4}{3}$, which is wrong.

Multiply the numerators together and the denominators together.

$\frac{10}{21} \times \frac{7}{15} = \frac{10 \times 7}{21 \times 15} = \frac{70}{315}$

Now simplify by the greatest common factor of $70$ and $315$, which is $35$.

$\frac{70}{315} = \frac{70 \div 35}{315 \div 35} = \frac{2}{9}$

To undo a multiplication by $\frac{3}{5}$, divide by $\frac{3}{5}$, which means multiplying by $\frac{5}{3}$.

$? = \frac{9}{20} \div \frac{3}{5} = \frac{9}{20} \times \frac{5}{3} = \frac{45}{60} = \frac{3}{4}$

Check: $\frac{3}{4} \times \frac{3}{5} = \frac{9}{20}$.

The divisor is what you divide the first fraction by, so divide $\frac{3}{8}$ by the result $\frac{9}{16}$.

$? = \frac{3}{8} \div \frac{9}{16} = \frac{3}{8} \times \frac{16}{9} = \frac{48}{72} = \frac{2}{3}$

Check: $\frac{3}{8} \div \frac{2}{3} = \frac{3}{8} \times \frac{3}{2} = \frac{9}{16}$.

Multiply all three numerators and all three denominators.

$\frac{2 \times 6 \times 7}{3 \times 7 \times 8} = \frac{84}{168}$

Now simplify by the greatest common factor $84$.

$\frac{84}{168} = \frac{84 \div 84}{168 \div 84} = \frac{1}{2}$

Multiply all three numerators and all three denominators.

$\frac{4 \times 5 \times 3}{5 \times 6 \times 8} = \frac{60}{240}$

Now simplify by the greatest common factor of $60$ and $240$, which is $60$.

$\frac{60}{240} = \frac{60 \div 60}{240 \div 60} = \frac{1}{4}$

Half of the recipe means $\frac{1}{2}$ of $\frac{2}{3}$ cup.

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

So you use $\frac{1}{3}$ cup, which is less than the full $\frac{2}{3}$, as expected for half a recipe.

Multiply the numerators together and the denominators together.

$\frac{3}{4} \times \frac{8}{15} = \frac{3 \times 8}{4 \times 15} = \frac{24}{60}$

Now simplify by the greatest common factor of $24$ and $60$, which is $12$.

$\frac{24}{60} = \frac{24 \div 12}{60 \div 12} = \frac{2}{5}$