Question

using multiplication to divide by a fraction
write the missing digits in the boxes to make each equation true.
1 $\frac{1}{2} div \frac{2}{3} = \frac{1}{2} \times \frac{square}{2} = \frac{3}{square}$
2 $\frac{4}{5} div \frac{1}{4} = \frac{4}{5} \times \frac{4}{square} = \frac{square}{square}$
3 $\frac{2}{5} div \frac{3}{4} = \frac{2}{5} \times \frac{square}{square} = \frac{square}{15}$
4 $\frac{5}{6} div \frac{5}{12} = \frac{5}{6} \times \frac{square}{square} = \frac{square}{30} = 2$
5 $\frac{3}{4} div \frac{5}{7} = \frac{3}{4} \times \frac{square}{square} = \frac{square}{square}$
6 $1\frac{1}{3} div \frac{3}{7} = \frac{square}{3} \times \frac{7}{square} = \frac{square}{square}$
7 $4\frac{square}{2} div \frac{2}{5} = \frac{9}{2} \times \frac{square}{square} = \frac{square}{square}$
8 $3\frac{1}{2} div \frac{square}{8} = \frac{7}{square} \times \frac{8}{7} = \frac{square}{square} = square$
9 $1\frac{2}{3} div 2\frac{1}{4} = \frac{square}{3} \times \frac{square}{9} = \frac{square}{square}$
10 $3\frac{3}{5} div 1\frac{3}{square} = \frac{18}{square} \times \frac{4}{7} = \frac{square}{square}$
11 write a word problem that could be solved by the equation in problem 8.

Explanation:

Step1: Use reciprocal for division

Dividing by a fraction = multiplying by its reciprocal. For $\frac{1}{2} \div \frac{2}{3}$, reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.
$\frac{1}{2} \times \frac{3}{2} = \frac{3}{4}$

Step2: Solve $\frac{4}{5} \div \frac{1}{4}$

Reciprocal of $\frac{1}{4}$ is $\frac{4}{1}$.
$\frac{4}{5} \times \frac{4}{1} = \frac{16}{5}$

Step3: Solve $\frac{2}{5} \div \frac{3}{4}$

Reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$.
$\frac{2}{5} \times \frac{4}{3} = \frac{8}{15}$

Step4: Solve $\frac{5}{6} \div \frac{5}{12}$

Reciprocal of $\frac{5}{12}$ is $\frac{12}{5}$.
$\frac{5}{6} \times \frac{12}{5} = \frac{60}{30} = 2$

Step5: Solve $\frac{3}{4} \div \frac{5}{7}$

Reciprocal of $\frac{5}{7}$ is $\frac{7}{5}$.
$\frac{3}{4} \times \frac{7}{5} = \frac{21}{20}$

Step6: Convert mixed number, solve $1\frac{1}{3} \div \frac{3}{7}$

Convert $1\frac{1}{3}$ to $\frac{4}{3}$. Reciprocal of $\frac{3}{7}$ is $\frac{7}{3}$.
$\frac{4}{3} \times \frac{7}{3} = \frac{28}{9}$

Step7: Convert mixed number, solve $4\frac{1}{2} \div \frac{2}{5}$

$4\frac{1}{2} = \frac{9}{2}$, reciprocal of $\frac{2}{5}$ is $\frac{5}{2}$.
$\frac{9}{2} \times \frac{5}{2} = \frac{45}{4}$

Step8: Convert mixed number, solve $3\frac{1}{2} \div \frac{7}{8}$

$3\frac{1}{2} = \frac{7}{2}$, reciprocal of $\frac{7}{8}$ is $\frac{8}{7}$.
$\frac{7}{2} \times \frac{8}{7} = \frac{56}{14} = 4$

Step9: Convert mixed numbers, solve $1\frac{2}{3} \div 2\frac{1}{4}$

$1\frac{2}{3} = \frac{5}{3}$, $2\frac{1}{4} = \frac{9}{4}$. Reciprocal of $\frac{9}{4}$ is $\frac{4}{9}$.
$\frac{5}{3} \times \frac{4}{9} = \frac{20}{27}$

Step10: Convert mixed numbers, solve $3\frac{3}{5} \div 1\frac{3}{4}$

$3\frac{3}{5} = \frac{18}{5}$, $1\frac{3}{4} = \frac{7}{4}$. Reciprocal of $\frac{7}{4}$ is $\frac{4}{7}$.
$\frac{18}{5} \times \frac{4}{7} = \frac{72}{35}$

Step11: Create word problem for Q8

Frame a scenario matching $3\frac{1}{2} \div \frac{7}{8}$: e.g., "A baker has $3\frac{1}{2}$ pounds of flour. Each cookie recipe uses $\frac{7}{8}$ pounds of flour. How many full batches of cookies can the baker make?"

Answer:

1. $\boldsymbol{\frac{1}{2} \div \frac{2}{3} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4}}$
2. $\boldsymbol{\frac{4}{5} \div \frac{1}{4} = \frac{4}{5} \times \frac{4}{1} = \frac{16}{5}}$
3. $\boldsymbol{\frac{2}{5} \div \frac{3}{4} = \frac{2}{5} \times \frac{4}{3} = \frac{8}{15}}$
4. $\boldsymbol{\frac{5}{6} \div \frac{5}{12} = \frac{5}{6} \times \frac{12}{5} = \frac{60}{30} = 2}$
5. $\boldsymbol{\frac{3}{4} \div \frac{5}{7} = \frac{3}{4} \times \frac{7}{5} = \frac{21}{20}}$
6. $\boldsymbol{1\frac{1}{3} \div \frac{3}{7} = \frac{4}{3} \times \frac{7}{3} = \frac{28}{9}}$
7. $\boldsymbol{4\frac{1}{2} \div \frac{2}{5} = \frac{9}{2} \times \frac{5}{2} = \frac{45}{4}}$
8. $\boldsymbol{3\frac{1}{2} \div \frac{7}{8} = \frac{7}{2} \times \frac{8}{7} = \frac{56}{14} = 4}$
9. $\boldsymbol{1\frac{2}{3} \div 2\frac{1}{4} = \frac{5}{3} \times \frac{4}{9} = \frac{20}{27}}$
10. $\boldsymbol{3\frac{3}{5} \div 1\frac{3}{4} = \frac{18}{5} \times \frac{4}{7} = \frac{72}{35}}$
11. Word Problem: A baker has $3\frac{1}{2}$ pounds of flour. Each cookie recipe uses $\frac{7}{8}$ pounds of flour. How many full batches of cookies can the baker make?