How to Divide Mixed Numbers? (+FREE Worksheet!)

Dividing Mixed Numbers – Example 1:

Find the quotient. \(2 \ \frac{1}{3} \div \ 1 \ \frac{1}{4}=\)

Solution:

Convert mixed numbers to fractions, \(2 \ \frac{1}{3} =\) \(\frac{7}{3}\), \( \ 1 \ \frac{1}{4}=\) \(\ \frac{5}{4}\)

Apply the fractions rule for dividing, \(\frac{7}{3} \div \frac{5}{4}=\) \(\frac{7}{3} × \frac{4}{5}=\ \frac{7 \ × \ 4}{3 \ × \ 5}=\frac{28}{15}=1 \ \frac{13}{15}\)

Dividing Mixed Numbers – Example 2:

Find the quotient. \(2 \ \frac{5}{6} \div \ 1 \ \frac{2}{5}=\)

Solution:

Convert mixed numbers to fractions, \(2 \ \frac{5}{6}=\) \(\frac{17}{6} \), \(\ 1 \ \frac{2}{5}=\) \(\frac{7}{5}\)

Use the fractions rule for dividing, \(\frac{17}{6} \div \frac{7}{5}\)\(= \frac{17}{6} × \frac{5}{7}= \frac{17 \ × \ 5}{6 \ × \ 7}=\frac{85}{42}=2 \ \frac{1}{42}\)

Dividing Mixed Numbers – Example 3:

Find the quotient. \(2 \ \frac{1}{2} \div \ 1 \ \frac{1}{5}=\)

Solution:

Convert mixed numbers to fractions, \(2 \ \frac{1}{2}=\) \(\frac{5}{2}\), \(\ 1 \ \frac{1}{5}=\) \(\frac{6}{5} \)

Use the fractions rule for dividing,\(\frac{5}{2} \div \frac{6}{5}=\) \(\frac{5}{2} × \frac{5}{6}= \frac{5×5}{2×6}= \frac{25}{12}=2 \ \frac{1}{12}\)

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Dividing Mixed Numbers – Example 4:

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Find the quotient. \(4 \ \frac{3}{4} \div \ 3 \ \frac{4}{5}=\)

Solution:

Converting mixed numbers to fractions, \(4 \ \frac{3}{4}=\) \(\frac{19}{4}\), \(\ 3 \ \frac{4}{5}=\) \(\frac{19}{5} \)

Use the fractions rule for dividing, \(\frac{19}{4} \div \frac{19}{5}=\) \(\frac{19}{4} × \frac{5}{19}= \frac{19×5}{4×19}=\frac{95}{76}=\frac {95\div 19} {76\div19}=\frac {5} {4}=1 \ \frac{1}{4}\)

Exercises for Dividing Mixed Numbers

Dividing Mixed Numbers

Find each quotient.

1. \(\color{blue}{2\frac{1}{5} \div 2\frac{1}{2}}\)
2. \(\color{blue}{2\frac{3}{5} \div 1\frac{1}{3}}\)
3. \(\color{blue}{3\frac{1}{6} \div 4\frac{2}{3}}\)
4. \(\color{blue}{1\frac{2}{3} \div 3\frac{1}{3}}\)
5. \(\color{blue}{4\frac{1}{8} \div 2\frac{2}{4}}\)
6. \(\color{blue}{3\frac{1}{2} \div 2\frac{3}{5}}\)

Download Multiplying and Dividing Mixed Numbers Worksheet

1. \(\color{blue}{\frac{22}{25}}\)
2. \(\color{blue}{1\frac{19}{20}}\)
3. \(\color{blue}{\frac{19}{28}}\)
4. \(\color{blue}{\frac{1}{2}}\)
5. \(\color{blue}{1\frac{13}{20}}\)
6. \(\color{blue}{1\frac{9}{26}}\)

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Watch this practice video for additional examples and reinforcement: