learning how to divide a fraction by a fraction
Number Framework Stage 8
Rulers
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.
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.
(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.
Examples: Draw pictures to find the answers to: 2 ÷ 1/4
2/3 ÷ 1/6
4 ÷ 1/2
3/2 ÷ 1/8 ...
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 ...
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
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...
A unit fraction has 1 for the numerator. Make up a whole number divided by a unit fraction problem and solve it.
What does x ÷ 1/Z equal? (Answer: xz.)
Printed from https://nzmaths.co.nz/resource/dividing-fractions at 7:20pm on the 28th April 2024