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

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.

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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

Why must I convert to an improper fraction before multiplying?

You cannot simply multiply \(\color{blue}{2 \frac{1}{2} \times 1 \frac{1}{3}}\) as \(\color{blue}{(2 \times 1)}\) + \(\color{blue}{(\frac{1}{2} \times \frac{1}{3})}\) — that gives the wrong answer. The correct approach requires treating the entire mixed number as one fraction. Converting to an improper fraction ensures you multiply the whole value, not just its parts separately.

Do I always need to simplify at the end?

Yes — GED answers are expected in simplest form. Always check whether the resulting improper fraction can be simplified before converting to a mixed number.

How does multiplying mixed numbers appear on the GED?

GED questions may involve real-world contexts: multiplying a mixed-number length by a mixed-number width, scaling a recipe, or calculating area. Recognizing the multiplication setup is as important as the computation.

Related Topics

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