Dividing Mixed Numbers

Dividing Mixed Numbers

You can divide mixed numbers in few simple and easy steps.

Step by step guide to divide mixed numbers

  1. Convert the mixed numbers to improper fractions. \(a \ \frac{c}{ \color{blue}{b} }= a \ \color{blue}{+} \ \frac{c}{\color{ blue }{b}}=\frac{a \color{ blue }{b} \ \color{blue}{+} \ c}{ \color{ blue }{b} }\)
  2. Divide fractions and simplify if necessary.

Example 1:

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

Solution :

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

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

Example 2:

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

Solution :

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

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

Example 3:

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

Solution :

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

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

Example 4:

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

Solution:

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

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

Exercises

Find each quotient.

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

Download Multiplying and Dividing Mixed Numbers Worksheet

Answers

  • \(\color{blue}{\frac{22}{25}}\)
  • \(\color{blue}{1\frac{19}{20}}\)
  • \(\color{blue}{\frac{19}{28}}\)
  • \(\color{blue}{\frac{1}{2}}\)
  • \(\color{blue}{1\frac{13}{20}}\)
  • \(\color{blue}{1\frac{9}{26}}\)

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