Recall that a mixed number is a number consisting of an integer and a unit fraction. A mixed number can also be expressed as an improper fraction or a fraction where the numerator is larger than the denominator.

Exploration

Watch the video below, where we discuss how to multiply and divide mixed numbers.

In what ways are the steps the same as multiplying and dividing other fractions?
In what ways are the steps different?

Notice that we can use the same steps for multiplying and dividing fractions that we previously saw, with one added step. That is, we can convert mixed numbers to improper fractions first.

Practice questions

Question 1

Evaluate $2\frac{2}{5}\cdot1\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.

Outcomes

6.NS.1

Interpret and compute quotients of fractions.

6.NS.1.a

Compute quotients of fractions by fractions, for example, by applying strategies such as visual fraction models, equations, and the relationship between multiplication and division, to represent problems.

6.NS.1.b

Solve real-world problems involving division of fractions by fractions.

2.03 Multiplying and dividing mixed numbers