Question

flip the second & multiply
rewrite each division problem as multiplication. then solve. write your answer in simplest form. the first one has been done for you.
1.
$\frac{1}{2} \div \frac{4}{5} = \frac{1}{2} \times \frac{5}{4} = \frac{5}{8}$
2.
$\frac{1}{8} \div \frac{4}{7} = \frac{1}{8} \times \
ule{1cm}{0.15mm} = \
ule{1cm}{0.15mm}$
3.
$\frac{5}{8} \div \frac{1}{3} = \frac{5}{8} \times \
ule{1cm}{0.15mm} = \
ule{1cm}{0.15mm}$
4.
$\frac{4}{9} \div \frac{5}{6} = \frac{4}{9} \times \
ule{1cm}{0.15mm} = \
ule{1cm}{0.15mm}$
5.
$\frac{7}{11} \div \frac{3}{8} = \frac{7}{11} \times \
ule{1cm}{0.15mm} = \
ule{1cm}{0.15mm}$
6.
$\frac{3}{10} \div \frac{5}{7} = \frac{3}{10} \times \
ule{1cm}{0.15mm} = \
ule{1cm}{0.15mm}$
7.
$\frac{3}{5} \div \frac{2}{5} = \frac{3}{5} \times \
ule{1cm}{0.15mm} = \
ule{1cm}{0.15mm}$
8.
$\frac{7}{9} \div \frac{3}{10} = \frac{7}{9} \times \
ule{1cm}{0.15mm} = \
ule{1cm}{0.15mm}$

Explanation:

Problem 2

Step1: Flip the second fraction

To divide by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{4}{7}$ is $\frac{7}{4}$. So, $\frac{1}{8} \div \frac{4}{7} = \frac{1}{8} \times \frac{7}{4}$.

Step2: Multiply the numerators and denominators

Multiply the numerators: $1 \times 7 = 7$. Multiply the denominators: $8 \times 4 = 32$. So, $\frac{1}{8} \times \frac{7}{4} = \frac{7}{32}$.

Step1: Flip the second fraction

The reciprocal of $\frac{1}{3}$ is $\frac{3}{1}$. So, $\frac{5}{8} \div \frac{1}{3} = \frac{5}{8} \times \frac{3}{1}$.

Step2: Multiply the numerators and denominators

Multiply the numerators: $5 \times 3 = 15$. Multiply the denominators: $8 \times 1 = 8$. So, $\frac{5}{8} \times \frac{3}{1} = \frac{15}{8}$.

Step1: Flip the second fraction

The reciprocal of $\frac{5}{6}$ is $\frac{6}{5}$. So, $\frac{4}{9} \div \frac{5}{6} = \frac{4}{9} \times \frac{6}{5}$.

Step2: Simplify and multiply

Simplify before multiplying: 4 and 5 have no common factors, 6 and 9 can be simplified by dividing by 3. So, $\frac{4}{9} \times \frac{6}{5} = \frac{4}{3} \times \frac{2}{5}$. Multiply the numerators: $4 \times 2 = 8$. Multiply the denominators: $3 \times 5 = 15$. So, $\frac{4}{9} \times \frac{6}{5} = \frac{8}{15}$.

Answer:

$\frac{7}{4}$, $\frac{7}{32}$

Problem 3