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.A.1

Interpret and compute quotients of fractions, and solve real-world and mathematical problems involving division of fractions by fractions (e.g., connecting visual fraction models and equations to represent the problem is suggested). For example, create a story context for (2/3) ÃƒÂ· (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÃƒÂ· (3/4) = 8/9 because 3/4 times 8/9 is 2/3 ((a/b) ÃƒÂ· (c/d) = ad/bc). Further example: How much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

2.03 Multiplying and dividing mixed numbers