Multiplying Mixed Numbers by Mixed Numbers: Step-by-Step Example
22 October 2026
Multiplying mixed numbers by mixed numbers can look tricky at first, but it becomes much easier when you break it down into clear steps. Here is a simple example to help your child see exactly how the process works.
Example question
Multiply 1 1/2 × 2 1/3.
Step 1: Change each mixed number to an improper fraction.
1 1/2 = (1 × 2 + 1) / 2 = 3/2.
2 1/3 = (2 × 3 + 1) / 3 = 7/3.
Step 2: Multiply the fractions.
3/2 × 7/3 = (3 × 7) / (2 × 3) = 21/6.
Step 3: Change the answer back to a mixed number.
21 divided by 6 is 3 with 3 left over. So, 21/6 = 3 3/6.
Step 4: Simplify the fraction if you can.
3/6 can be simplified to 1/2.
So, 3 3/6 = 3 1/2.
The correct answer is 3 1/2.
| Step | Working | Result |
|---|---|---|
| Change 1 1/2 to improper fraction | 1 × 2 + 1 = 3, over 2 | 3/2 |
| Change 2 1/3 to improper fraction | 2 × 3 + 1 = 7, over 3 | 7/3 |
| Multiply the fractions | 3/2 × 7/3 = (3 × 7) / (2 × 3) | 21/6 |
| Change to mixed number | 21 ÷ 6 = 3 remainder 3 | 3 3/6 |
| Simplify the fraction | 3/6 = 1/2 | 3 1/2 |
Now your child can spot each stage when multiplying two mixed numbers: changing to improper fractions, multiplying, and simplifying the answer. They are ready to practise this type of question themselves.
