Fractions Times Whole Numbers

Achievement Objectives
NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
NA5-3: Understand operations on fractions, decimals, percentages, and integers.
Specific Learning Outcomes

Find fractions of whole number amounts using multiplication and division.

Solve multiplication and division problems that involve fractions.

Description of Mathematics

Number Framework Stages 7 and 8.

Required Resource Materials
Fraction materials.

Using Materials

Problem: “A caterer at a wedding supplies 5 pavlovas. At the end of the wedding, she  sees 3 quarters of all the pavlovas have been eaten. How many pavlovas were eaten?”

Write ¾ x 5 on the board. Then students model wholes that can be cut into quarters:

Then they show ¾ of each pavlova being eaten:


Discuss why pavlovas were eaten.

Discuss why ¾ x 5 = 15/4 = 3 3/4.

Examples: Word problems for: ¾ x 2 2/5 x 3 5/6 x 3 ¾ x 4

Using Imaging

Do these by imaging. Fold back to building the fractions if needed.
Examples: Word stories for: ¾ x 3 2/3 x 3 2/3 x 5 3/5 x 4

Using Number Properties

Problem: “Look at the answers to the examples above and work out how to find 3/5 x 7 by using the numbers alone.” (Answer: 3/5 x 7 = 21/5 = 4 1/5.)
Examples: Word stories for: 3/10 x 5 8/9 x 7 11/12 x 4 3/8 x 16

Problem: “Work out 10/11 x 3 and 3 x 10/11. What do you notice?”
(Answer: Reversing the order of multiplication does not alter the answer even though fractions are involved.)

Understanding Number Properties:

What letters replace the question marks? g x h/i = (?x?)/? (Answer: (gxh)/i.)

Understanding Number Properties:

What letters replace the question marks? h/i x g = (?x?)/? (Answer: (hxg)/i.)

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