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

Fractions greater than \(1\) are usually represented as mixed numbers. In this case, the mixed number consists of an integer part and a standard fraction less than \(1\). The integer part is the same as the quotient part and the numerator of the fraction is the remainder of the division and the denominator of the fraction will also be the divisor. 

Related Topics

• How to Simplify Fractions
• How to Multiply and Divide Fractions
• How to Add Mixed Numbers
• How to Subtract Mixed Numbers
• How to Multiply Mixed Numbers

Step by step guide to dividing mixed numbers

In the division of mixed numbers, their improper fractions can be used instead, and if necessary, the result can be converted back to the form of mixed numbers.

Here’s how to divide mixed numbers:

• Step 1: Convert all mixed numbers into improper fractions: To convert a mixed number to a fraction, you must first multiply the mixed number by the denominator, then add the result to the numerator. Put the resulting number in the case of a new numerator and keep the denominator of the same fraction as the previous one. This way you have converted a mixed number into a fraction. \(a \ \frac{c}{ \color{blue}{b} }= a \ \color{blue}{+} \ \frac{c}{\color{ blue }{b}}=\frac{a \color{ blue }{b} \ \color{blue}{+} \ c}{ \color{ blue }{b} }\)
• Step 2: Divide these two improper fractions: To divide fractions, we turn the division into a multiplication problem by multiplying the first fraction by the inverse of the second fraction (reciprocal).
• Step 3: Convert the answer to a mixed number: To convert a fraction larger than one to a mixed number, you must divide the numerator by the denominator. After division, the obtained quotient is the same integer in the mixed number and the remainder of the division is the numerator of the fraction. The denominator is also the denominator of the initial fraction in the mixed number.

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,\(\frac{5}{2} \div \frac{6}{5}=\) \(\frac{5}{2} × \frac{5}{6}= \frac{5×5}{2×6}= \frac{25}{12}=2 \ \frac{1}{12}\)

Dividing Mixed Numbers – Example 4:

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

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. \(\color{blue}{1\frac{9}{26}}\)