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Level Four > Number and Algebra

# Fractions Times Whole Numbers

Achievement Objectives:

Achievement Objective: NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
AO elaboration and other teaching resources
Achievement Objective: NA5-3: Understand operations on fractions, decimals, percentages, and integers.
AO elaboration and other teaching resources

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.
Activity:

#### 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.)