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

How to multiply 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.

Multiplying mixed numbers is a key fraction skill for the GED Mathematical Reasoning test. The process is straightforward: convert each mixed number to an improper fraction first, then multiply across. This lesson walks you through every step with worked examples and practice problems so you are fully prepared for test day.

What Does It Mean to Multiply Mixed Numbers?

A mixed number like \(\color{blue}{2 \frac{1}{2}}\) combines a whole number and a fraction. To multiply two mixed numbers, you must first rewrite each as an improper fraction, because you cannot multiply whole-number parts and fraction parts separately. Once both numbers are improper fractions, you multiply numerators together and denominators together, then simplify.

How to Multiply Mixed Numbers

Step 1: Convert to improper fractions

Multiply the whole number by the denominator, add the numerator, and write the result over the original denominator.

• \(\color{blue}{2 \frac{1}{2} = \frac{(2 \times 2 + 1)}{2} = \frac{5}{2}}\)
• \(\color{blue}{1 \frac{1}{3} = \frac{(1 \times 3 + 1)}{3} = \frac{4}{3}}\)

Step 2: Multiply numerators and denominators

\(\color{blue}{\frac{5}{2} \times \frac{4}{3} = \frac{20}{6}}\)

Step 3: Simplify

\(\color{blue}{\frac{20}{6} = \frac{10}{3} = 3 \frac{1}{3}}\)

Tip: Cross-cancel before multiplying

You can simplify diagonally before multiplying to keep numbers smaller: in \(\color{blue}{\frac{5}{2} \times \frac{4}{3}}\), cancel 2 and 4 (both divisible by 2) → \(\color{blue}{\frac{5}{1} \times \frac{2}{3} = \frac{10}{3}}\). Same answer, fewer steps.

Step-by-Step Summary

1. Convert each mixed number to an improper fraction.
2. Cross-cancel common factors if possible.
3. Multiply numerators; multiply denominators.
4. Convert the result back to a mixed number and simplify.

Watch: Multiplying Mixed Numbers (Video Lesson)

Math Antics demonstrates multiplying mixed numbers with step-by-step visual examples:

Multiplying Mixed Numbers – Worked Examples

Example 1: Multiply \(\color{blue}{2 \frac{1}{2} \times 1 \frac{1}{3}}\).

Convert: \(\color{blue}{2 \frac{1}{2} = \frac{5}{2}}\), \(\color{blue}{1 \frac{1}{3} = \frac{4}{3}}\).
Multiply: \(\color{blue}{\frac{5}{2} \times \frac{4}{3} = \frac{20}{6} = \frac{10}{3}}\).
Convert: \(\color{blue}{10 \div 3 = 3}\) R \(\color{blue}{1}\). Answer: \(\color{blue}{3 \frac{1}{3}}\).

Example 2: Multiply \(\color{blue}{3 \frac{1}{4} \times 2 \frac{2}{5}}\).

Convert: \(\color{blue}{3 \frac{1}{4} = \frac{13}{4}}\), \(\color{blue}{2 \frac{2}{5} = \frac{12}{5}}\).
Multiply: \(\color{blue}{\frac{13}{4} \times \frac{12}{5} = \frac{156}{20} = \frac{39}{5}}\).
Convert: \(\color{blue}{39 \div 5 = 7}\) R \(\color{blue}{4}\). Answer: \(\color{blue}{7 \frac{4}{5}}\).

Example 3: Multiply \(\color{blue}{1 \frac{2}{3} \times 2 \frac{1}{4}}\).

Convert: \(\color{blue}{1 \frac{2}{3} = \frac{5}{3}}\), \(\color{blue}{2 \frac{1}{4} = \frac{9}{4}}\).
Cross-cancel: 3 and 9 share factor 3 → \(\color{blue}{\frac{5}{1} \times \frac{3}{4} = \frac{15}{4}}\).
Convert: \(\color{blue}{15 \div 4 = 3}\) R \(\color{blue}{3}\). Answer: \(\color{blue}{3 \frac{3}{4}}\).

Example 4: Multiply \(\color{blue}{4 \frac{1}{2} \times 2 \frac{2}{3}}\).

Convert: \(\color{blue}{4 \frac{1}{2} = \frac{9}{2}}\), \(\color{blue}{2 \frac{2}{3} = \frac{8}{3}}\).
Cross-cancel: 9 and 3 share factor 3; 2 and 8 share factor 2 → \(\color{blue}{\frac{3}{1} \times \frac{4}{1} = 12}\).
Answer: \(\color{blue}{12}\).

More Practice: How to Multiply Mixed Numbers (Video)

Khan Academy provides additional examples and explains why the improper-fraction method works:

Exercises for Multiplying Mixed Numbers

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

Answers

1. \(\color{blue}{\frac{5}{2} \times \frac{4}{3} = \frac{20}{6} = \frac{10}{3} = 3 \frac{1}{3}}\)
2. \(\color{blue}{\frac{7}{2} \times \frac{7}{5} = \frac{49}{10} = 4 \frac{9}{10}}\)
3. \(\color{blue}{\frac{9}{4} \times \frac{10}{3} = \frac{90}{12} = \frac{15}{2} = 7 \frac{1}{2}}\)
4. \(\color{blue}{\frac{11}{6} \times \frac{12}{5} = \frac{132}{30} = \frac{22}{5} = 4 \frac{2}{5}}\)
5. \(\color{blue}{\frac{9}{2} \times \frac{5}{3} = \frac{45}{6} = \frac{15}{2} = 7 \frac{1}{2}}\)

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Frequently Asked Questions

What is the first step in multiplying mixed numbers?

Change each mixed number into an improper fraction. Multiply the whole number by the denominator and add the numerator, keeping the same denominator, so 3 1/5 becomes 16/5. You cannot just multiply the whole parts and the fraction parts separately, because that skips the cross terms and gives an answer that is too small.

Can you multiply mixed numbers without converting them?

Yes, by using the distributive property or an area model with partial products. For 1 1/2 × 2 1/3, multiply each part by each part: 1 × 2 = 2, 1 × 1/3 = 1/3, 1/2 × 2 = 1, and 1/2 × 1/3 = 1/6. Adding gives 3 1/2. Converting first, 3/2 × 7/3 = 21/6, gives the same 3 1/2.

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

Write the whole number over 1, convert the mixed number, then multiply. For 3 × 2 1/4, rewrite as 3/1 × 9/4 = 27/4, which is 6 3/4. You can also think of it as three groups of 2 1/4: three 2s make 6 and three 1/4s make 3/4, giving the same 6 3/4.

How do you multiply mixed numbers with different denominators?

You do not need a common denominator to multiply. Convert to improper fractions and multiply straight across. For 1 1/3 × 2 1/4, write 4/3 × 9/4. Cross-cancel the 4s and reduce 9 and 3 to 3 and 1, leaving 1/1 × 3/1 = 3. Common denominators matter only when you add or subtract.

How is multiplying mixed numbers different from multiplying fractions?

Multiplying mixed numbers adds one step before and sometimes one after. Before, you convert to improper fractions; after, you may turn an improper answer like 17/6 back into 2 5/6. The middle step, multiplying numerators together and denominators together, is exactly the same as with proper fractions, and cross-canceling works the same way.

Related Topics

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