Multiplying whole numbers with fractions

General

Students learn to multiply a whole number by a fraction.

Common core standard(s)

CCSS.Math.Content.5.NF.B

Relevance

It is important to be able to learn how to multiply a whole by a fraction so you can determine, for example, how many slices of pizza you have.

Introduction

Have students simplify the fractions as much as possible, either by turning it into a mixed number or simplification of the fraction.

Development

Show students the three pizzas on the interactive whiteboard. Explain that each pizza has been cut into 8 slices. Every pizza now has 7 slices left. How many slices of pizza are there in total? You have 3 times 7 slices. The multiplication problem is 3 x 7 = 21. That gives you 21 times 1//8 portion of a pizza. The fraction is 21//8. Convert the fraction greater than 1 into a mixed number - you know that a whole pizza has 8 slices- and you get 2 whole pizzas with 5 slices left over. The mixed number is 2 5//8. Ask students to solve the following problems individually. Show the problem 6 x 2//3. Explain that you can choose to solve this problem in two ways. Walk through both ways with the students, and then explain to students that they can decide for each problem which method they want to use. Both are equally good and students can choose the one they like best. Ask students to solve the following problems individually. Discuss the method they chose and have them explain their thinking. Then given students the fraction story problem. Make sure that students are able to find the fraction in the word problem as well as the whole number they are multiplying by. Then have students practice two fraction word problems.

Check that students are able to multiply whole numbers by fractions by asking the following question:
- Which methods can you use to multiply a whole number by a fraction?

Guided practice

Students are first given a multiplication problem with visual support. They then are given a multiplication problem without visual support. They then get fraction story problems to solve. Ask students to explain their strategy for all of the different problems.

Closing

Discuss with students the importance of being able to multiply whole numbers by fractions. To close, ask student to spin a number using the spinner on the interactive whiteboard. They then select a box and then must multiply their number by the fraction as represented by the pizza.

Teaching tips

Students who have difficulty multiplying a whole number with a fraction can start by practicing multiplication with a simple fraction like 1//2 or 1//3. You can also use a fraction circle or bar to help visually support their learning.