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Level Five > Number and Algebra

# Ratios with Whole Numbers

Keywords:
Achievement Objectives:

Achievement Objective: Use rates and ratios.

Specific Learning Outcomes:

Solve problems involving ratios.

Description of mathematics:

Number Framework Stage 8

Required Resource Materials:
Ratios with whole numbers (Material Master 8-27)
Activity:

Students, and indeed some textbook writers, often confuse ratios and fractions because of the similarity of their equivalence laws. For example, 3 : 4 = 12 : 16 is speciously the same as 3/4 = 12/16.

To avoid this confusion, ratios are introduced to students as 3 or more quantities rather than 2.

### Using Number Properties

Problem: “Georgie sees a cake recipe in a book. She writes it as the ratio 3 : 1 : 2 : 100 : 150 : 1. Georgie wants to make 3 cakes.   Write the ingredients needed as a ratio.”

(Answer: Everything is tripled so 9 : 3 : 6 : 300 : 450 : 3 is the recipe for 3 cakes.)

Problem: “Walter plans to make a very large cake with the recipe.

He plans to use the ratio 30 : 10 : 20 : 1 000 : 500 : 10. Walter has made a mistake in his calculations? What is the mistake?”

(Answer: Walter should be multiplying all quantities by 10. So for butter 10 x 150 = 1 500 not 500.)

Problem: “Three university students paint a house in their holidays to earn money. They don’t all work the same hours. Jude works for 40 hours. Look at the pay slip and decide how long Melanie and Aaron worked for.”

Discuss how to reduce 400 : 800 : 600 to its lowest equivalent ratio.

(Answer: Link this to the HCF of 400, 800, 600 being 200.  So 400 : 800 : 600 = 2 : 4 : 3 by dividing all numbers by  200.  So 2 : 4 : 3 = 20 : 40 : 30 by multiplying through by 10. So  Melanie has worked for 20 hours and Aaron has worked for 30 hours.)

Examples: Worksheet (Material Master 8–27).

#### Understanding Number Properties:

Are the ratios 3a : 3b : 3 c and a : b : c the same? Explain.

## Hot Shots

Solve problems involving ratios.

## Tree-mendous Measuring

Solve problems involving ratios.

## Extending Mixing Colours

Solve problems involving ratios.

## Extending Hotshots

Solve problems involving ratios.

## Combining Proportions

Solve problems involving ratios.