When we multiply fractions by the rule, we are able to multiply our numerators together, and multiply our denominators together. When we have mixed fractions, we can express them as improper fractions first, and then we are able to multiply them by the rule. We don't actually have to, but it means we have less work to do. Who doesn't like that idea?

What about division?

Sure! We can also express mixed numbers as improper fractions, to help with division. Once we've done that, we can use the rule for dividing fractions. Remember that rule? We can multiply by the reciprocal of a fraction, when we need to divide by a fraction.

Seeing it in action

In this video, we multiply and divide mixed numbers, by expressing them as improper fractions.

Worked Examples

Question 1

Evaluate $2\frac{2}{5}\times1\frac{3}{5}$225×135, giving your answer as a mixed number in simplest form.

Question 2

Evaluate $3\frac{3}{7}\div1\frac{3}{5}$337÷135, giving your answer as a mixed number in simplest form.

Both together!

This time, we have a multiplication and a division in the same problem, but you'll see it's possible to do it all by changing our mixed fractions (also called mixed numbers) to improper fractions.

Question 3

Evaluate $4\frac{5}{9}\times3\frac{4}{9}\div\frac{3}{5}$459×349÷35, writing your answer in its simplest form.

Outcomes

9D.NA2.01

Simplify numerical expressions involving integers and rational numbers, with and without the use of technology