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

  • Convert the mixed numbers to improper fractions. \(a \ \frac{c}{ \color{blue}{b} }= a \ \color{blue}{+} \ \frac{c}{\color{ blue }{b}}=\frac{a \color{ blue }{b} \ \color{blue}{+} \ c}{ \color{ blue }{b} }\)
  • 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.

  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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