Dividing Fractions

The Ministry is migrating nzmaths content to Tāhurangi.           
Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz). 
When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024. 
e-ako maths, e-ako Pāngarau, and e-ako PLD 360 will continue to be available. 

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

Achievement Objectives
NA5-3: Understand operations on fractions, decimals, percentages, and integers.
Specific Learning Outcomes

learning how to divide a fraction by a fraction

Description of Mathematics

Number Framework Stage 8

Required Resource Materials
Squared paper

Rulers

Activity

Students normally regard division as sharing. The other meaning of division is measurement, namely finding the number of equal sets that can be made. This is the most useful view for making sense of division by a fraction.

Using Materials

Problem: “Susie has 3 cakes. She intends giving her friends 1/3 of a cake each. What is 3 ÷ 1/3?” Get the students to draw rectangular cakes and divide each cake into thirds.

thjirds.

(Circles are more complicated to work with.) Discuss why 3 ÷ 1/3 = 9. So, Susie can feed 9 people.

Problem: “Malcolm has 3/4 of a cake. He gives guests 1/8 of a cake each. How many guests get a piece of cake?” Write 3/4 ÷ 1/8 on the board. Get the students to draw 3/4 and add lines to create eighths.
Discuss how the drawing shows 3/4 ÷ 1/8 = 6.

eighths.

Examples: Draw pictures to find the answers to: 2 ÷ 1/4
2/3 ÷ 1/6
4 ÷ 1/2
3/2 ÷ 1/8 ...
 

Using Imaging

Problem: “Describe a picture showing 3/8. Imagine what you would do to solve 3/8 ÷ 1/16.”

Examples: Imagine pictures to find the answers to: 3 ÷ 1/4
5/3 ÷ 1/6
5 ÷ 1/4
1/2 ÷ 1/6 ...

Using Number Properties

Problem: “Janice tries to work out 6/8 ÷ 1/8. Reading 6/8 ÷ 1/8 out loud as 6 eighths divided by 1 eighth, she immediately sees the answer is 6. How?”
(Answer: 6 objects divided by 1 object is always 6 regardless of what the objects are. So ÷ = 6.)

Examples:
9/17 ÷ 1/17
34/81 ÷ 1/81
89/108 ÷ 1/108
46/3 ÷ 1/3
67/5 ÷ 1/5

Understanding Number Properties

What does a/b ÷ 1/b equal for any choice of a and b? (Answer: a, since any number divided by 1 gives that same number.)

Problem: “Janice now tries to apply her method to harder divisions like 3/4 ÷ 1/8. She claims 3/4 ÷ 1/8 = 6/8 ÷ 1/8. And so the answer must be 6. Is she correct?” (Answer: Yes.3/4 = 6/8)

Examples: Work out:
3/4 ÷ 1/16
5/3 ÷ 1/6
2/3 ÷ 1/12
7/8 ÷ 1/4
5 ÷ 1/4...

Understanding Number Properties

A unit fraction has 1 for the numerator. Make up a whole number divided by a unit fraction problem and solve it.

 

Understanding Number Properties

What does x ÷ 1/Z equal? (Answer: xz.)

Add to plan

Log in or register to create plans from your planning space that include this resource.


Level Five