G7_Ratio and Proportion

​Unit 12 _______________________________________Grade 7

​Learning Objectives

​• simplify and compare ratios

​• divide an amount into two parts in a given ratio

​• use the unitary method to solve problems involving ratio and direct proportion

Multiple Choice

What is the ratio of green squares to blue squares in its simplest form?

• 4 : 6

• 6 : 4

• 2 : 3

• 3 : 2

Multiple Select

Which of these ratios is/are equivalent to 1 : 2? Select all that possible

• 2 : 4

• 3 : 5

• 7 : 14

• 6 : 3

• 10 : 20

Multiple Choice

One pen cost 80 cents. How much does it cost to buy 5 pens?

• 50 cents

• 100 cents

• 200 cents

• 400 cents

Multiple Choice

A 5 litre tin of paint covers 20 square metres of wall. How many square metres of wall will 15 litres of the same paint cover?

• 4 square metres

• 15 square metres

• 60 square metres

• 100 square metres

​12.1 Simplifying Ratios

The ratio of red to yellow is 1 : 3​

1 : 3 is read as "1 to 3"

​A ratio written in its simplest form must not contain any decimals or fractions.

Multiple Choice

What is the ratio of blue to green?

• 2 : 4

• 4 : 2

• 1 : 2

• 2 : 1

Multiple Choice

What is the ratio of green to blue?

• 2 : 3

• 3 : 2

• 4 : 6

• 6 : 4

​12.2 Sharing in Ratios

​12.2 Sharing in Ratios

Multiple Choice

In a class of 33 students, the ratio of boys to girls is 4 : 7.

How many girls are in the class?

• 11

• 12

• 21

• 24

Multiple Choice

If Johan and Renee share $90 in the ratio 7 : 3, how much money will Renee have?

• $9

• $10

• $27

• $63

Multiple Choice

$75 is to be shared in the ratio 1 : 4.

What is the value of 1 part?

• $75

• $25

• $15

• $5

​12.3 Using Direct Proportion

​Two quantities are in direct proportion when their ratio stays the same as the quantities increase or decrease.

​

​One packet of rice costs $3.25, so two packets of rice cost twice as much.

​Two packets of rice cost 2 × $3.25 = $6.50.

​

Six tickets to a concert cost $120, so three tickets cost half as much.

Three tickets cost $120 ÷ 2 = $60.

​The method used in part a is called the unitary method because you find the cost of one book then use this to find the cost of 10 books.

​egg : cupcake = 2 : 12 = 1 : 6

​So, 1 egg is for 6 cupcake

​

​36 : 6 = 6 OR 6 eggs are needed to make 36 cupcakes

​

Multiple Choice

There are three people in each tent at a campsite.

If there are five tents, how many people are there?

• 2

• 3

• 5

• 15

Multiple Choice

A bag of fruit in the supermarket contains 4 oranges and 9 apples.

You buy enough bags to get 32 oranges.

How many apples will you get?

• 8

• 9

• 32

• 72

Multiple Choice

A pair of shoes costs $25.

How much do three pairs of these shoes cost?

• $3

• $15

• $50

• $75