**Ratio and Proportion**

**Ratio and Proportions**

Example 1

2/9 spectators at a football match are children. The ratio of the number of men to the number of women is 7:3. There are 800 more adults than children. How many more men than women are there at the football match?

Example 2

Ratio and Proportion

What is the difference between ratio and proportion?

In a wardrobe, there are 81 shirts and coats. The ratio of shirts to coats is 7 : 2. Each shirt costs $56. Each coat costs 2 3/4 times as much as a shirt. Find the total cost of coats.

Example 4

Example 5

Example 6

Example 6

Example 6

2 units

7 units

Difference in units between adults and children

7 - 2 = 5 units

5 units

800 adults

1 unit

800 ÷ 5 = 160

Total number of adults

7 units

7 units

160 X 7 = 1120

There were 1120 adults at the football match

Ratio of Men to Women is 7: 3

Difference in parts between men and women

7 - 3 = 4 parts

Total number of parts representing men and women

7 + 3 = 10 parts

10 parts represent the total number of adults at the football match

10 parts

1120 adults

1 part

1120 ÷ 10 = 112

4 parts

112 X 4 = 448 men

There were 448 more men than women in the football match

2/9 spectators at a football match are children. The ratio of the number of men to the number of women is 7:3. There are 800 more adults than children. How many more men than women are there at the football match?

The commander-trainee ratio in a police academy is 7 : 330. The number of female police trainees is 3/8 the number of male trainees. There are 7, 200 male trainees. How many commanders are there in the police academy?

Total number of male and female trainees = 7200 + 2700

= 9900

The commander-trainee ratio is 7 : 330

7

330

=>

Total number of commanders

Total number trainees

=

7 X

?

330 X

?

330 X ? = 9900

? =

9900

330

= 30

=

7 X

30

Working

330 X

30

=

210

9900

There are 210 commanders in the police academy

Number of female trainees =

3

8

X

7200

= 2700

1 : 2

Ratio

1

2

Proportion

1

2

or 50%

2

5

or 40%

2 : 5

7 units

5 parts

7+ 2 = 9 units

9 units

81

(shirts + coats)

1 unit

81

÷

9

2 units

= 18 coats

= 9

9 X 2

Total cost of coats = (2 3/4 X 56) X 18

= $2, 772

Total number of units in the ratio 7 : 2

= 154 X 18

Example 3

Ron, Wayne and Victor raised a sum of money for their school building fund. Ron raised 3/8 of the sum. The remaining was raised by Wayne and Victor in the ratio 14 : 11. Ron raised $324 more than Victor. How much money did they raise altogether?

3/8

Ron

Wayne & Victor

14 : 11

Wayne : Victor

Total units (Wayne and Victor)

14 + 11 =

25

units

5 parts

25

units

1 part

25

÷ 5 = 5 units

3 parts (Ron)

5 X 3 =

15

units

Total number of units from Ron, Wayne and Victor

15

+

25

= 40 units

Difference (in units) between the contribution of Ron and Victor

15 - 11 = 3 units

3 units

$324

1 unit

$324 ÷ 3 = $81

40 units

$81 X 40 = $3240

Ron, Wayne and Victor raised $3, 240 altogehter

Example 4

Example 5

At the beginning of a party, there were 84 girls. The ratio of girls to boys was 3 : 2. Halfway through the party, more boys joined the party. As a result, the ratio of boys to girls became 7 : 3. How many boys joined the party?

Before

After

At the beginning of a party, there were 84 girls. The ratio of girls to boys was 3 : 2. Halfway through the party, more boys joined the party. As a result, the ratio of boys to girls became 7 : 3. How many boys joined the party?

Difference in units between boys:

7 - 2 = 5 units

3 units

84 girls

1 unit

84 ÷ 3 = 28

5 units

28 X 5 = 140 boys

140 boys joined the party.

At the beginning of a party, there were 84 girls. The ratio of girls to boys was 3 : 2. Halfway through the party, more boys joined the party. As a result, the ratio of boys to girls became 4 : 2. How many boys joined the party?

Before

After

At the beginning of a party, there were 84 girls. The ratio of girls to boys was 3 : 2. Halfway through the party, more

boys joined. As a result, the ratio of boys to girls became 4 : 2. How many boys joined the party?

Before

After

2 : 3

B : G

4 : 2

B : G

If only they were equal......

2

X 2

: 3

X 2

4

X 3

: 2

X 3

4 :

6

12 :

6

B : G

B : G

6 units

84 girls

1 unit

84 ÷ 6 = 14

12 - 4 = 8 units

8 units

14 X 8 = 112 boys

112 boys joined the party

Difference in units between boys: