Multiplying and Dividing Fractions: Additional Practice (Set 1)

Multiply the numerators together and the denominators together.

$\frac{7}{8} \times \frac{2}{3} = \frac{7 \times 2}{8 \times 3} = \frac{14}{24}$

Now simplify by the greatest common factor of $14$ and $24$, which is $2$.

$\frac{14}{24} = \frac{14 \div 2}{24 \div 2} = \frac{7}{12}$

Dividing by $\frac{3}{5}$ means multiplying by its reciprocal $\frac{5}{3}$.

$\frac{9}{10} \div \frac{3}{5} = \frac{9}{10} \times \frac{5}{3} = \frac{45}{30} = \frac{3}{2}$

The last step divides top and bottom by $15$. Multiplying without flipping would give $\frac{27}{50}$, which is wrong.

Each 'of' is a multiplication, so multiply all three fractions at once.

$\frac{3}{4} \times \frac{2}{3} \times \frac{8}{9} = \frac{3 \times 2 \times 8}{4 \times 3 \times 9} = \frac{48}{108}$

Now simplify by the greatest common factor of $48$ and $108$, which is $12$.

$\frac{48}{108} = \frac{48 \div 12}{108 \div 12} = \frac{4}{9}$

To undo a multiplication by $\frac{4}{5}$, divide by $\frac{4}{5}$, which means multiplying by $\frac{5}{4}$.

$? = \frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$

Check: $\frac{5}{6} \times \frac{4}{5} = \frac{20}{30} = \frac{2}{3}$.

Dividing by $\frac{4}{3}$ means multiplying by its reciprocal $\frac{3}{4}$.

$\frac{8}{9} \div \frac{4}{3} = \frac{8}{9} \times \frac{3}{4} = \frac{24}{36} = \frac{2}{3}$

The last step divides top and bottom by $12$. Multiplying without flipping would give $\frac{32}{27}$, which is wrong.

Multiply all three numerators and all three denominators.

$\frac{2 \times 9 \times 4}{3 \times 16 \times 5} = \frac{72}{240}$

Now simplify by the greatest common factor of $72$ and $240$, which is $24$.

$\frac{72}{240} = \frac{72 \div 24}{240 \div 24} = \frac{3}{10}$

Write $12 = \frac{12}{1}$ and multiply by the reciprocal of $\frac{4}{5}$.

$12 \div \frac{4}{5} = \frac{12}{1} \times \frac{5}{4} = \frac{60}{4} = 15$

Multiplying by $\frac{4}{5}$ instead would give $\frac{48}{5}$, which is wrong.

'Of' means multiply, so compute $\frac{3}{5}$ of $\frac{5}{6}$.

$\frac{3}{5} \times \frac{5}{6} = \frac{15}{30} = \frac{1}{2}$

The runner went $\frac{1}{2}$ mile. Adding the fractions instead would give $\frac{8}{11}$, which is wrong.

Write $21 = \frac{21}{1}$ and multiply straight across.

$\frac{6}{7} \times 21 = \frac{6 \times 21}{7} = \frac{126}{7} = 18$

A quick check: $\frac{1}{7}$ of $21$ is $3$, and six sevenths is $6 \times 3 = 18$.

Write the whole number as $10 = \frac{10}{1}$, then divide by multiplying by its reciprocal $\frac{1}{10}$.

$\frac{5}{6} \div 10 = \frac{5}{6} \times \frac{1}{10} = \frac{5}{60} = \frac{1}{12}$

The last step divides top and bottom by $5$. Dividing by a whole number larger than the fraction makes it smaller, as expected.

Multiply the numerators together and the denominators together.

$\frac{14}{15} \times \frac{25}{21} = \frac{14 \times 25}{15 \times 21} = \frac{350}{315}$

Now simplify by the greatest common factor of $350$ and $315$, which is $35$.

$\frac{350}{315} = \frac{350 \div 35}{315 \div 35} = \frac{10}{9}$

Dividing by $\frac{14}{25}$ means multiplying by its reciprocal $\frac{25}{14}$.

$\frac{7}{10} \div \frac{14}{25} = \frac{7}{10} \times \frac{25}{14} = \frac{175}{140} = \frac{5}{4}$

The last step divides top and bottom by $35$. Multiplying without flipping would give $\frac{98}{250}$, which is wrong.