Question

dividing fractions by fractic
grade 5 fractions worksheet
find the quotients.

1. $\frac{3}{5} \div \frac{2}{3} = $
2. $\frac{2}{6} \div \frac{3}{5} = $
3. $\frac{1}{4} \div \frac{1}{5} = $
4. $\frac{1}{5} \div \frac{5}{6} = $
5. $\frac{1}{3} \div \frac{3}{6} = $
6. $\frac{4}{6} \div \frac{2}{6} = $
7. $\frac{1}{4} \div \frac{4}{5} = $
8. $\frac{1}{6} \div \frac{2}{3} = $
9. $\frac{3}{5} \div \frac{1}{4} = $

Explanation:

Step1: Recall fraction division rule

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. So \( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} \) (where \( b
eq0, c
eq0, d
eq0 \)).

Step2: Solve \( \frac{3}{5} \div \frac{2}{3} \)

Using the rule, \( \frac{3}{5} \div \frac{2}{3} = \frac{3}{5} \times \frac{3}{2} \). Multiply numerators: \( 3\times3 = 9 \), multiply denominators: \( 5\times2 = 10 \). So \( \frac{3}{5} \div \frac{2}{3} = \frac{9}{10} \).

Step3: Solve \( \frac{2}{6} \div \frac{3}{5} \)

First, simplify \( \frac{2}{6} \) to \( \frac{1}{3} \) (optional, but easier). Then \( \frac{1}{3} \div \frac{3}{5} = \frac{1}{3} \times \frac{5}{3} = \frac{5}{9} \). Wait, no—wait, original \( \frac{2}{6} \times \frac{5}{3} = \frac{10}{18} = \frac{5}{9} \)? Wait, no: \( \frac{2}{6} \times \frac{5}{3} = \frac{10}{18} = \frac{5}{9} \)? Wait, no, \( 2\times5 = 10 \), \( 6\times3 = 18 \), simplify \( \frac{10}{18} = \frac{5}{9} \). Wait, but maybe better to do as is: \( \frac{2}{6} \div \frac{3}{5} = \frac{2}{6} \times \frac{5}{3} = \frac{10}{18} = \frac{5}{9} \).

Step4: Solve \( \frac{1}{4} \div \frac{1}{5} \)

Using the rule: \( \frac{1}{4} \times \frac{5}{1} = \frac{5}{4} \) (or \( 1\frac{1}{4} \)).

Step5: Solve \( \frac{1}{5} \div \frac{5}{6} \)

\( \frac{1}{5} \times \frac{6}{5} = \frac{6}{25} \).

Step6: Solve \( \frac{1}{3} \div \frac{3}{6} \)

Simplify \( \frac{3}{6} \) to \( \frac{1}{2} \). Then \( \frac{1}{3} \div \frac{1}{2} = \frac{1}{3} \times \frac{2}{1} = \frac{2}{3} \). Wait, original \( \frac{1}{3} \div \frac{3}{6} = \frac{1}{3} \times \frac{6}{3} = \frac{6}{9} = \frac{2}{3} \).

Step7: Solve \( \frac{4}{6} \div \frac{2}{6} \)

\( \frac{4}{6} \times \frac{6}{2} \). The 6s cancel: \( \frac{4}{1} \times \frac{1}{2} = \frac{4}{2} = 2 \).

Step8: Solve \( \frac{1}{4} \div \frac{4}{5} \)

\( \frac{1}{4} \times \frac{5}{4} = \frac{5}{16} \).

Step9: Solve \( \frac{1}{6} \div \frac{2}{3} \)

\( \frac{1}{6} \times \frac{3}{2} = \frac{3}{12} = \frac{1}{4} \).

Step10: Solve \( \frac{3}{5} \div \frac{1}{4} \)

\( \frac{3}{5} \times \frac{4}{1} = \frac{12}{5} = 2\frac{2}{5} \).

Answer:

1. \( \boldsymbol{\frac{9}{10}} \)
2. \( \boldsymbol{\frac{5}{9}} \)
3. \( \boldsymbol{\frac{5}{4}} \) (or \( 1\frac{1}{4} \))
4. \( \boldsymbol{\frac{6}{25}} \)
5. \( \boldsymbol{\frac{2}{3}} \)
6. \( \boldsymbol{2} \)
7. \( \boldsymbol{\frac{5}{16}} \)
8. \( \boldsymbol{\frac{1}{4}} \)
9. \( \boldsymbol{\frac{12}{5}} \) (or \( 2\frac{2}{5} \))