Question

ks learning
dividing fractions by fractions
grade 5 fractions worksheet
find the quotients.

1. \\(\frac{3}{5} \div \frac{2}{3} =\\)
2. \\(\frac{2}{6} \div \frac{1}{5} =\\)
3. \\(\frac{2}{6} \div \frac{3}{5} =\\)
4. \\(\frac{4}{8} \div \frac{1}{4} =\\)
5. \\(\frac{1}{4} \div \frac{1}{5} =\\)
6. \\(\frac{2}{4} \div \frac{1}{4} =\\)
7. \\(\frac{1}{5} \div \frac{5}{6} =\\)
8. \\(\frac{2}{6} \div \frac{1}{8} =\\)
9. \\(\frac{1}{3} \div \frac{3}{6} =\\)
10. \\(\frac{3}{4} \div \frac{4}{5} =\\)
11. \\(\frac{4}{6} \div \frac{2}{6} =\\)
12. \\(\frac{1}{3} \div \frac{1}{4} =\\)
13. \\(\frac{1}{4} \div \frac{4}{5} =\\)
14. \\(\frac{3}{8} \div \frac{2}{3} =\\)
15. \\(\frac{1}{6} \div \frac{2}{3} =\\)
16. \\(\frac{1}{3} \div \frac{4}{6} =\\)
17. \\(\frac{3}{5} \div \frac{1}{4} =\\)
18. \\(\frac{2}{4} \div \frac{7}{8} =\\)
19. \\(\frac{4}{5} \div \frac{2}{5} =\\)
20. \\(\frac{4}{6} \div \frac{1}{3} =\\)

Explanation:

Step1: Recall the rule for dividing fractions

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. The formula is $\frac{a}{b} \div \frac{c}{d}=\frac{a}{b}\times\frac{d}{c}=\frac{ad}{bc}$ (where $b
eq0$, $c
eq0$, $d
eq0$).

Step2: Solve each problem using the rule

1) $\frac{3}{5}\div\frac{2}{3}$

Multiply by reciprocal: $\frac{3}{5}\times\frac{3}{2}=\frac{3\times3}{5\times2}=\frac{9}{10}$

2) $\frac{2}{6}\div\frac{1}{5}$

Simplify $\frac{2}{6}=\frac{1}{3}$, then multiply by reciprocal: $\frac{1}{3}\times\frac{5}{1}=\frac{5}{3}$

3) $\frac{2}{6}\div\frac{3}{5}$

Simplify $\frac{2}{6}=\frac{1}{3}$, multiply by reciprocal: $\frac{1}{3}\times\frac{5}{3}=\frac{5}{9}$

4) $\frac{4}{8}\div\frac{1}{4}$

Simplify $\frac{4}{8}=\frac{1}{2}$, multiply by reciprocal: $\frac{1}{2}\times\frac{4}{1}=\frac{4}{2} = 2$

5) $\frac{1}{4}\div\frac{1}{5}$

Multiply by reciprocal: $\frac{1}{4}\times\frac{5}{1}=\frac{5}{4}$

6) $\frac{2}{4}\div\frac{1}{4}$

Simplify $\frac{2}{4}=\frac{1}{2}$, multiply by reciprocal: $\frac{1}{2}\times\frac{4}{1}=\frac{4}{2}=2$ (or directly: $\frac{2}{4}\div\frac{1}{4}=\frac{2}{4}\times\frac{4}{1}=2$)

7) $\frac{1}{5}\div\frac{5}{6}$

Multiply by reciprocal: $\frac{1}{5}\times\frac{6}{5}=\frac{6}{25}$

8) $\frac{2}{6}\div\frac{1}{8}$

Simplify $\frac{2}{6}=\frac{1}{3}$, multiply by reciprocal: $\frac{1}{3}\times\frac{8}{1}=\frac{8}{3}$

9) $\frac{1}{3}\div\frac{3}{6}$

Simplify $\frac{3}{6}=\frac{1}{2}$, multiply by reciprocal: $\frac{1}{3}\times\frac{2}{1}=\frac{2}{3}$

10) $\frac{3}{4}\div\frac{4}{5}$

Multiply by reciprocal: $\frac{3}{4}\times\frac{5}{4}=\frac{15}{16}$

11) $\frac{4}{6}\div\frac{2}{6}$

Multiply by reciprocal: $\frac{4}{6}\times\frac{6}{2}=\frac{4}{2}=2$

12) $\frac{1}{3}\div\frac{1}{4}$

Multiply by reciprocal: $\frac{1}{3}\times\frac{4}{1}=\frac{4}{3}$

13) $\frac{1}{4}\div\frac{4}{5}$

Multiply by reciprocal: $\frac{1}{4}\times\frac{5}{4}=\frac{5}{16}$

14) $\frac{3}{8}\div\frac{2}{3}$

Multiply by reciprocal: $\frac{3}{8}\times\frac{3}{2}=\frac{9}{16}$

15) $\frac{1}{6}\div\frac{2}{3}$

Multiply by reciprocal: $\frac{1}{6}\times\frac{3}{2}=\frac{3}{12}=\frac{1}{4}$

16) $\frac{1}{3}\div\frac{4}{6}$

Simplify $\frac{4}{6}=\frac{2}{3}$, multiply by reciprocal: $\frac{1}{3}\times\frac{3}{2}=\frac{3}{6}=\frac{1}{2}$

17) $\frac{3}{5}\div\frac{1}{4}$

Multiply by reciprocal: $\frac{3}{5}\times\frac{4}{1}=\frac{12}{5}$

18) $\frac{2}{4}\div\frac{7}{8}$

Simplify $\frac{2}{4}=\frac{1}{2}$, multiply by reciprocal: $\frac{1}{2}\times\frac{8}{7}=\frac{8}{14}=\frac{4}{7}$

19) $\frac{4}{5}\div\frac{2}{5}$

Multiply by reciprocal: $\frac{4}{5}\times\frac{5}{2}=\frac{20}{10}=2$

20) $\frac{4}{6}\div\frac{1}{3}$

Simplify $\frac{4}{6}=\frac{2}{3}$, multiply by reciprocal: $\frac{2}{3}\times\frac{3}{1}=\frac{6}{3}=2$

Answer:

1. $\boldsymbol{\frac{9}{10}}$
2. $\boldsymbol{\frac{5}{3}}$
3. $\boldsymbol{\frac{5}{9}}$
4. $\boldsymbol{2}$
5. $\boldsymbol{\frac{5}{4}}$
6. $\boldsymbol{2}$
7. $\boldsymbol{\frac{6}{25}}$
8. $\boldsymbol{\frac{8}{3}}$
9. $\boldsymbol{\frac{2}{3}}$
10. $\boldsymbol{\frac{15}{16}}$
11. $\boldsymbol{2}$
12. $\boldsymbol{\frac{4}{3}}$
13. $\boldsymbol{\frac{5}{16}}$
14. $\boldsymbol{\frac{9}{16}}$
15. $\boldsymbol{\frac{1}{4}}$
16. $\boldsymbol{\frac{1}{2}}$
17. $\boldsymbol{\frac{12}{5}}$
18. $\boldsymbol{\frac{4}{7}}$
19. $\boldsymbol{2}$
20. $\boldsymbol{2}$