 Multiplying fractions

# Multiplying fractions

I can multiply a fraction by another fraction.

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## General

Students learn how to multiply fractions.

## Common core standard(s)

CCSS.Math.Content.5.NF.B

## Relevance

It is important to be able to multiply fractions so you can determine, for example, how large each slice of apple is.

## Introduction

Ask students to solve the problems in which they must multiply a whole number by a fraction or a fraction by a whole number.

## Development

Remind students that a fraction is made up of a numerator and a denominator. Show the problem 2//3 x 3//4. Show the fraction bar divided into 4 units. 3 of the units are colored. Explain that this fraction bar shows 3//4. Then show that you will divide each unit into 3 smaller units, and two of them have been colored dark blue. This is 2//3 of the fraction. Now show the large table and emphasize that 2//3 x 3//4 is the same as 2//3 of 3//4. Now count the number of dark blue squares and the total number of squares. The total table has 12 squares, of which 6 are dark blue. So 6 of the 12 squares are dark blue which makes the fraction 6//12. The final step is to simplify the fraction. 6//12 = 1//2. Ask students to solve the following problems and explain their thinking. Next show students the problem 2//5 x 3//6. Explain that you first multiply the numerators (2 x 3 = 6). Next you multiply the denominators ( 5 x 6 = 30). The fraction is 6//30 which simplified = 1//5. Ask students to solve the following problems and explain their strategy. Show students how to multiply a mixed number by a fraction. Explain that you first multiply the whole by the fraction. Then you multiply the fractions (1//2 x 1//5). Then you set the whole and fraction together to create the total (1 1//10). Have students do the next problems individually. Show the problem 2//4 x 1//4 x 3//5. Explain to students that you multiply from left to right. First you solve 2//4 x 1//4. You then use the answer 2//16 to multiply by the next fraction (2//16 x 3//5 = 6//80 simplified to 3//40). Ask students to solve the next problems individually. Then explain to students how to solve a fraction story problem- first determining which numbers are needed to solve, saying or writing the problem, and then solving by multiplying the fractions. Two more fraction word problems follow for students to practice individually or in pairs.

Check that students are able to multiply fractions by asking teh following question:
- Which steps do you take to multiply fractions together?

## Guided practice

Students are given fraction multiplication problems, first with visual support, then in the abstract and then students also get fraction word problems to solve.

## Closing

Discuss the importance of being able to multiply fractions. To close, ask students to spin all four dials to create a fraction multiplication problem. Students must then solve the created problem. You can choose to have the first student with the correct answer come up to spin the dials for the next problem.

## Teaching tips

Students who have difficulty multiplying fractions can first practice visualizing fractions. Try to make it visible (or tangible) that a fraction is a portion or unit of a whole, like the apple example. Have them create a table for each fraction, drawing in the lines and coloring in the boxes.

## Instruction materials

Optional: a fraction chart or worksheet with blank tables for students to use for fraction multiplication. 