Writing and Simplifying Ratios

Writing and Simplifying Ratios

Multiple Choice

A recipe for shortbread requires 300 g of plain flour, 100 g of sugar and 200 g of butter. Suppose you wish to make some shortbread following this recipe using 300 g of sugar. How much flour and butter will you need?

• Flour: 300g

  Butter: 200g

• Flour: 600g

  Butter: 400g

• Flour: 900g

  Butter: 600g

• Flour: 1200g

  Butter: 800g

What are ratios?

A ratio is a comparison of two or more amounts often written using a : symbol (colon).

The order in which the ratio is stated must be made clear. For example, the recipe for shortbread has flour: sugar: butter = 3:1:2

Part: Part ratios and Part: Whole ratios

A Part: Part ratios compares separate parts of a whole. For example, green: red = 4:3

A Part: Whole ratio compares a part (or parts) to a whole. For example, red marbles: all marbles in the bag = 3:10 Primary colour marbles (RGB) : all marbles in the bag = 9:10

Multiple Choice

The pet shop has 2 dogs, 4 cats, and 5 hamsters. What is the ratio of dogs to all pets?

• 2:4

• 2:5

• 2:4:5

• 2:11

Ratios, fractions and percentages

Part: Whole ratios are often expressed as fractions or percentages of the whole.

Apples : All fruits = 4: 10 = 2: 5
The number of apples is  $\frac{2}{5}$  or  $40\%$  of all fruits.

Simplifying ratios

Ratios that represent same proportions are equivalent ratios.

To write a ratio in simplest form, divide each number in the ratio by the highest common factor (HCF).

Multiple Choice

Kelly has 20 apps on her iPad. 8 are school apps, 4 are music apps, and 8 are games. What is the ratio of school apps to entertainment apps in simplest form?

• 8:20

• 8:12

• 2:5

• 2:3

• 1:1

Ratio writing conventions

Ratios should be written in simplest form, using whole numbers only (no fractions, percentages or decimals).

Multiple Choice

Rewrite 4.9 : 21 in simplest form.

• 49:21

• 49:210

• 7:3

• 7:30

Ratios and Units

Usually ratios are used to compare quantities of the same type, such as lengths, mass, etc.

Each quantity in the ratio must be expressed in the same units, which should not be written.

Practice Time

Textbook Page 209 Ex. 4.1

Textbook Page 214 Ex. 4.2

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