How to Multiply Mixed Numbers (Step-by-Step)

Learning how to multiply mixed numbers is an important next step after multiplying fractions and multiplying fractions by whole numbers. This skill combines several fraction concepts and helps students deepen their understanding of how fractions greater than 1 work.

In this post, we’ll break down multiplying mixed numbers into clear, manageable steps that support both understanding and accuracy.

What Are Mixed Numbers?

A mixed number is a number made up of a whole number and a fraction.

Example:

This represents 2 whole units and one-third of another.

Why Mixed Numbers Must Be Converted Before Multiplying

Mixed numbers cannot be multiplied directly. Before multiplying, they must be rewritten as improper fractions.

This ensures that the entire value of the mixed number is included in the multiplication.

Step 1: Rewrite Each Mixed Number as an Improper Fraction

To convert a mixed number to an improper fraction:

1. Multiply the whole number by the denominator
2. Add the numerator
3. Place the result over the original denominator

Example:

Step 2: Multiply the Fractions

Once both mixed numbers are written as improper fractions, multiply the numerators and denominators.

Example:

Step 3: Simplify the Product

Simplify the fraction if possible.

Step 4: Convert to a Mixed Number (If Needed)

If required, rewrite the improper fraction as a mixed number.

Another Example

Using Visual Models to Multiply Mixed Numbers

Area models and fraction diagrams can help students visualize mixed number multiplication. Breaking mixed numbers into whole and fractional parts allows students to see how the product grows larger than one whole.

Common Mistakes Students Make

• Forgetting to convert mixed numbers to improper fractions
• Errors when converting mixed numbers
• Forgetting to simplify
• Skipping the final conversion back to a mixed number

Addressing these mistakes helps students stay accurate and confident.

Teaching Tips for Multiplying Mixed Numbers

• Review improper fractions before teaching this skill
• Encourage students to estimate answers first
• Use visuals to reinforce understanding
• Practice converting between mixed numbers and improper fractions

How This Skill Fits Into Fraction Learning

Multiplying mixed numbers builds on:

• Multiplying fractions
• Multiplying fractions by whole numbers
• Converting between mixed numbers and improper fractions

This skill represents an important milestone in fraction mastery.

Raven's Thoughts

Learning how to multiply mixed numbers helps students combine multiple fraction skills into one process. By converting to improper fractions, multiplying carefully, simplifying, and converting back when needed, students can solve these problems with confidence.

With clear instruction and consistent practice, multiplying mixed numbers becomes a manageable and logical extension of fraction multiplication.