# 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.

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

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