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

How to divide mixed numbers, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

Dividing mixed numbers is a fraction skill that appears frequently on the GED Mathematical Reasoning test. The method builds on what you already know about dividing fractions: convert, flip, and multiply. Once you can divide simple fractions, dividing mixed numbers requires only one extra step, converting to improper fractions first.

What Does It Mean to Divide Mixed Numbers?

Dividing by a mixed number asks “how many times does this value fit into that value?” For example, \(\color{blue}{3 \frac{1}{2} \div 1 \frac{3}{4}}\) asks how many \(\color{blue}{1 \frac{3}{4}}\)-unit lengths fit into \(\color{blue}{3 \frac{1}{2}}\) units. The answer is found by converting both to improper fractions, then multiplying the first fraction by the reciprocal (the flipped version) of the second.

How to Divide Mixed Numbers

Step 1: Convert both to improper fractions

• \(\color{blue}{3 \frac{1}{2} = \frac{7}{2}}\)
• \(\color{blue}{1 \frac{3}{4} = \frac{7}{4}}\)

Step 2: Multiply by the reciprocal

Division becomes multiplication when you flip the second fraction (the divisor):

\(\color{blue}{\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}}\)

• \(\color{blue}{\frac{7}{2} \div \frac{7}{4} = \frac{7}{2} \times \frac{4}{7} = \frac{28}{14} = 2}\)

Step 3: Simplify

Reduce the result and, if greater than 1, convert to a mixed number.

Step-by-Step Summary

1. Convert each mixed number to an improper fraction.
2. Keep the first fraction, \(\color{blue}{\text{ change } \div \text{ to }}\) ×, flip the second fraction (use its reciprocal).
3. Cross-cancel common factors if possible.
4. Multiply numerators; multiply denominators.
5. Simplify and convert back to a mixed number if needed.

Watch: Dividing Mixed Numbers (Video Lesson)

Khan Academy walks through dividing mixed numbers with clear worked examples:

Dividing Mixed Numbers – Worked Examples

Example 1: Divide \(\color{blue}{3 \frac{1}{2} \div 1 \frac{3}{4}}\).

Convert: \(\color{blue}{3 \frac{1}{2} = \frac{7}{2}}\), \(\color{blue}{1 \frac{3}{4} = \frac{7}{4}}\).
Flip and multiply: \(\color{blue}{\frac{7}{2} \times \frac{4}{7} = \frac{28}{14} = 2}\).

Example 2: Divide \(\color{blue}{2 \frac{2}{3} \div 1 \frac{1}{3}}\).

Convert: \(\color{blue}{2 \frac{2}{3} = \frac{8}{3}}\), \(\color{blue}{1 \frac{1}{3} = \frac{4}{3}}\).
Flip and multiply: \(\color{blue}{\frac{8}{3} \times \frac{3}{4} = \frac{24}{12} = 2}\).

Example 3: Divide \(\color{blue}{4 \frac{1}{2} \div 1 \frac{1}{2}}\).

Convert: \(\color{blue}{4 \frac{1}{2} = \frac{9}{2}}\), \(\color{blue}{1 \frac{1}{2} = \frac{3}{2}}\).
Flip and multiply: \(\color{blue}{\frac{9}{2} \times \frac{2}{3} = \frac{18}{6} = 3}\).

Example 4: Divide \(\color{blue}{5 \frac{1}{4} \div 2 \frac{1}{8}}\).

Convert: \(\color{blue}{5 \frac{1}{4} = \frac{21}{4}}\), \(\color{blue}{2 \frac{1}{8} = \frac{17}{8}}\).
Flip and multiply: \(\color{blue}{\frac{21}{4} \times \frac{8}{17} = \frac{168}{68} = \frac{42}{17}}\).
Convert: \(\color{blue}{42 \div 17 = 2}\) R \(\color{blue}{8}\). Answer: \(\color{blue}{2 \frac{8}{17}}\).

More Practice: Dividing Mixed Numbers and Fractions (Video)

This Khan Academy video covers dividing mixed numbers and fractions together, with additional real-world examples:

Exercises for Dividing Mixed Numbers

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

Answers

1. \(\color{blue}{\frac{7}{2} \times \frac{4}{7} = \frac{28}{14} = 2}\)
2. \(\color{blue}{\frac{8}{3} \times \frac{3}{4} = \frac{24}{12} = 2}\)
3. \(\color{blue}{\frac{9}{2} \times \frac{2}{3} = \frac{18}{6} = 3}\)
4. \(\color{blue}{\frac{21}{4} \times \frac{8}{17} = \frac{168}{68} = \frac{42}{17} = 2 \frac{8}{17}}\)
5. \(\color{blue}{\frac{6}{1} \times \frac{2}{3} = \frac{12}{3} = 4}\)

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Frequently Asked Questions

What is the first step in dividing mixed numbers?

The first step is to convert every mixed number to an improper fraction. Multiply the whole number by the denominator, add the numerator, and keep the same denominator. For example, 2 2/3 becomes (2 × 3 + 2)/3 = 8/3. Once both numbers are improper fractions, you can divide them just like ordinary fractions.

How do you divide mixed numbers step by step?

Convert both mixed numbers to improper fractions, keep the first fraction, change ÷ to ×, flip the second fraction, then multiply and simplify. For 4 1/2 ÷ 1 1/2, write 9/2 ÷ 3/2, change it to 9/2 × 2/3 = 18/6, and simplify to 3. That makes sense, since 1 1/2 fits into 4 1/2 exactly three times.

How is dividing mixed numbers like dividing fractions?

After the conversion step, it is exactly the same process. Dividing fractions means multiplying by the reciprocal, and mixed numbers follow that rule once they are written as improper fractions. The only new skill is the conversion at the start and, if needed, turning an improper answer back into a mixed number at the end, such as 11/4 = 2 3/4.

How do you divide a mixed number by a whole number?

Write the whole number as a fraction over 1, then divide as usual. For 3 3/4 ÷ 3, rewrite as 15/4 ÷ 3/1, flip the divisor to get 15/4 × 1/3 = 15/12, and simplify to 5/4, or 1 1/4. A quick check: 1 1/4 × 3 = 3 3/4, which matches the starting number.

How do you divide a mixed number by a fraction?

Convert the mixed number, then multiply by the reciprocal of the fraction. For 1 1/4 ÷ 1/8, write 5/4 × 8/1 = 40/4 = 10. In words, ten pieces that are each 1/8 long fit into 1 1/4. Dividing by a fraction less than 1 always gives an answer larger than the starting number.

Can you divide mixed numbers without making improper fractions?

Sometimes, by changing them to decimals instead. For 2 1/2 ÷ 1 1/4, write 2.5 ÷ 1.25, which equals 2. This only works neatly when the fractions have short decimal forms like halves, fourths or fifths. Thirds and sevenths repeat forever, so improper fractions are the more reliable method for most test and homework problems.

Related Topics

• Multiplying Mixed Numbers
• Convert Between Improper Fractions and Mixed Numbers
• Simplifying Fractions
• Word Problems Fractions
• Order of Decimals Mixed Numbers and Fractions