Multiplying and Dividing Fractions: Practice

Multiply the numerators together and the denominators together.

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

Now simplify by the greatest common factor of $24$ and $36$, which is $12$.

$\frac{24}{36} = \frac{24 \div 12}{36 \div 12} = \frac{2}{3}$

Dividing by $\frac{1}{4}$ means multiplying by its reciprocal $\frac{4}{1}$.

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

There are two quarters in one half. Multiplying instead of dividing would give $\frac{1}{8}$, which is wrong.

Multiply the numerators together and the denominators together.

$\frac{2}{3} \times \frac{9}{10} = \frac{2 \times 9}{3 \times 10} = \frac{18}{30}$

Now simplify by the greatest common factor of $18$ and $30$, which is $6$.

$\frac{18}{30} = \frac{18 \div 6}{30 \div 6} = \frac{3}{5}$

Dividing by $\frac{4}{5}$ means multiplying by its reciprocal $\frac{5}{4}$.

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

The last step divides top and bottom by $2$. Multiplying without flipping would give $\frac{8}{15}$, which is wrong.

Multiply the numerators together and the denominators together.

$\frac{3}{8} \times \frac{4}{9} = \frac{3 \times 4}{8 \times 9} = \frac{12}{72}$

Now simplify by the greatest common factor of $12$ and $72$, which is $12$.

$\frac{12}{72} = \frac{12 \div 12}{72 \div 12} = \frac{1}{6}$

Dividing by $\frac{1}{6}$ means multiplying by its reciprocal $\frac{6}{1}$.

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

There are two sixths in one third. Multiplying instead of dividing would give $\frac{1}{18}$, which is wrong.

Multiply the numerators together and the denominators together.

$\frac{2}{3} \times \frac{3}{8} = \frac{2 \times 3}{3 \times 8} = \frac{6}{24}$

Now simplify by the greatest common factor of $6$ and $24$, which is $6$.

$\frac{6}{24} = \frac{6 \div 6}{24 \div 6} = \frac{1}{4}$

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

$\frac{3}{8} \div \frac{3}{4} = \frac{3}{8} \times \frac{4}{3} = \frac{12}{24} = \frac{1}{2}$

The last step divides top and bottom by $12$. Multiplying without flipping would give $\frac{9}{32}$, which is wrong.

Dividing by $\frac{1}{3}$ means multiplying by its reciprocal $\frac{3}{1}$.

$\frac{2}{9} \div \frac{1}{3} = \frac{2}{9} \times \frac{3}{1} = \frac{6}{9} = \frac{2}{3}$

The last step divides top and bottom by $3$. Multiplying without flipping would give $\frac{2}{27}$, which is wrong.

Dividing by $\frac{7}{16}$ means multiplying by its reciprocal $\frac{16}{7}$.

$\frac{7}{8} \div \frac{7}{16} = \frac{7}{8} \times \frac{16}{7} = \frac{112}{56} = 2$

The sevens cancel and $16 \div 8 = 2$. Multiplying without flipping would give $\frac{49}{128}$, which is wrong.

Multiply the numerators together and the denominators together.

$\frac{4}{9} \times \frac{3}{8} = \frac{4 \times 3}{9 \times 8} = \frac{12}{72}$

Now simplify by the greatest common factor of $12$ and $72$, which is $12$.

$\frac{12}{72} = \frac{12 \div 12}{72 \div 12} = \frac{1}{6}$

Dividing by $\frac{5}{6}$ means multiplying by its reciprocal $\frac{6}{5}$.

$\frac{5}{12} \div \frac{5}{6} = \frac{5}{12} \times \frac{6}{5} = \frac{30}{60} = \frac{1}{2}$

The last step divides top and bottom by $30$. Multiplying without flipping would give $\frac{25}{72}$, which is wrong.