Multiplying Mixed Numbers

Turn each mixed number into an improper fraction first, then multiply as usual.

An example

1 1/2 × 2 is 3/2 × 2, which is 6/2, which is 3.

Estimate before starting

2 1/4 × 3 is roughly 2 × 3, so about 6. That catches a wildly wrong answer.

Scaling still applies

A mixed number is more than 1, so multiplying by one always makes things bigger.

Convert to improper fractions first

For 2 1/2 × 1 1/3, write them as 5/2 and 4/3, then multiply: 20/6 = 10/3 = 3 1/3. Converting first is the reliable route, because it turns the problem into the straightforward numerator-times-numerator rule.

Why you cannot multiply the parts separately

2 1/2 × 1 1/3 is not 2 × 1 and 1/2 × 1/3. The area picture shows why: the rectangle has four regions, and multiplying the parts separately counts only two of them. This is the same reason 34 × 27 needs four partial products, not two.

Estimate with the whole numbers

2 1/2 × 1 1/3 is between 2 × 1 = 2 and 3 × 2 = 6, and probably nearer 3. The answer 3 1/3 fits. Bracketing the answer between two whole-number products is a quick way to check a mixed-number multiplication.

Simplify before multiplying

In 5/2 × 4/3, the 2 and the 4 share a factor of 2, so you can cancel first: 5/1 × 2/3 = 10/3. Simplifying before multiplying keeps the numbers small and reduces the chance of an arithmetic slip. It is optional but it is what experienced people do.