Ratio and Proportion

LESSON – RATIO AND PROPORTION

TOPIC

• Introduction

• Application of Ratio

• Family Size and Resources

• Direct and Indirect Proportion

• Population and Allocation

• Lesson Evaluation

 

INTRODUCTION 

Ratio is used to compare two or more values or qualities that are alike.

There are 12 blue boxes and 8 white boxes.

Ratios can be represented in the following ways:

• Use the ” : “ to separate the values: 12 : 8.

• Use the word ” to “: 12 to 8.

• Write it like a fraction: 12/8.

 

For example,

The ratio of blue boxes to white boxes is 12 to 8 or 12 : 8.

The ratio of white boxes to blue boxes is 8 to 12 or 8 : 12.

12 : 8 can be further simplify to 12/4 : 8/4 = 3 : 2.

That’s, 12 : 8 is equivalent (equal) to 3: 2.

 

WORKING EXAMPLES 

STRAWBERRIES 

 

 

ORANGES 

 

 

 

1. What is the total number of fruits?

2. What is the total number of strawberries?

3. What is the total number of oranges?

4. What is the ratio of oranges to strawberries?

5. What is the ratio of strawberries to oranges?

6. What is the ratio of oranges to total fruit?

7. What is the ratio of strawberries to total fruit?

 

FURTHER EXERCISE – QUANTITATIVE 

SAMPLE 

A. 12 : 16 = 3 : 4

B. 2 : 5 = 8 : 20

 

QUESTIONS

• ____ : 12 = 9 : 4

• 3 : 6 = 9 : ____

• ____ : 20 = 6 : 40

• 10 : 4 = ____ : 8

• 1 : ____ = 6 : 24

 

ANSWER KEY 

• 28 : 12 = 9 : 4

• 3 : 6 = 9 : 18

• 3 : 20 = 6 : 40

• 10 : 4 = 20 : 8

• 1 : 4 = 6 : 24

 

 

APPLICATION OF RATIO TO REAL LIFE SITUATION 

WORKING EXAMPLE 1 – The ratio of boys to girls in a class is 6 : 5. There are 24 boys. How many girls are in the class?

 

SOLUTION

Given,

Number of boys in the class is 24

Number of girls in the class?

Ratio of boys to girls is 6 : 5

 

Therefore, equivalent ratio is

6 : 5 = 24 : ____

6 : 5 = 6 x 4 : ____

6 x 4 : 5 x 4 = 24 : 20

The number of girls in the class is 20.

 

WORKING EXAMPLE 2 – Books are sold at 3 for  ₦25. Praise bought 9 books. How much did she pay?

 

SOLUTION 

Given

Cost of 3 books at  ₦25.

Cost of 9 books?

Ratio of 3 books to 9 books is  ₦25 :  ₦?

That’s, 3 : 9 = ₦25 :  ₦? (equivalent ratio)

3 x 1 : 3 x 3 = ₦25 x 1 : ₦25 x 3

3 : 1 : 9 = ₦25 : ₦75

Therefore, cost of 9 books is ₦75.

 

WORKING EXERCISE 

1. The ratio of teachers to pupils in a school is 1 : 5. How many teachers are in the school if the number of pupils is 100?

2. In a school setting, the ratio of girls to boys was 5 : 4. There were 40 girls?

 

[ a ] How many are boys?

[ b ] How many pupils were there all together?

[ c ] What is the ratio of boys to girls?

[ d ] What is the ratio of boys to total number of pupils in the school?

 

RATIO OF FAMILY SIZE AND RESOURCES 

ACTIVITY 1 – FAMILY SIZE AND RESOURCES 

Family with large size spend more to enjoy better facilities in terms of feeding, clothing and shelter as families with small size spend less to enjoy the same facilities.

 

WORKING EXAMPLE – John’s family size is 8 and he earns ₦48,000 monthly. Find the ratio of his family size to his monthly salary.

 

SOLUTION

8 : ₦48,000 = 1 : ₦6,000,

Each member of the family get care worth of ₦6,000.

• If his family size is 4, each member will get care worth of ₦12,000.

• If his family size is 12, each member will get care worth of ₦4,000.

• The more the family size gets bigger, the less each member of the family get.

 

POPULATION AND ALLOCATION 

WORKING EXAMPLE – In Lagos State, the budgetary allocation for education is ₦975,000,000 of the total population of 30,000. Find the amount allocated to education.

 

SOLUTION

Ratio of population to education budget is 30,000 : ₦975,000,000,

= 30,000 : ₦975,000,000

= 30 : ₦975,000

= 3 : ₦97,500

= 1 : ₦32,500

Each citizen enjoys education resources worth of ₦32,500.

 

RATIO OF PREVALENCE OF HIV/AIDS BETWEEN SEXES AND STATES OR COUNTRY 

WORKING EXAMPLE – In a state of 25,000 people, 50 of them are HIV positive. Find the ratio of infected people to the population.

 

SOLUTION 

Total population of people is 25,000

HIV infected people is 50

The ratio of infected people to the total population is 50 : 25,000,

That’s

5 : 2,500

= 1 : 500

Therefore, in every 500 people there is 1 HIV infected.

See the recommended books for further exercises.

 

PROPORTION 

A proportion is an equation in which two ratios are set equal to each other.

There are 3 types of proportion,

1. Direct proportion

2. Indirect proportion

3. Inverse proportion

 

DIRECT PROPORTION 

Directly proportion, an increase in one quantity causes an increase another at the same rate.

For example,

If the cost of one exercise book is ₦40.

Two books is ₦80,

Three books is ₦120, and so on.

As the qualities increase, the cost increases as well.

 

WORKING EXAMPLE 1 – The cost of 3 books is ₦80. Find the cost of 24 books.

 

SOLUTION

Cost of 3 books is ₦80

Cost of 6 books is ₦160

Cost of 9 books is ₦240

Cost of 12 books is ₦320

Cost of 15 books is ₦400

 

Cost of 18 books is ₦480

Cost of 21 books is ₦560

Cost of 24 books is ₦640.Therefore, cost of 24 books is 24/3 x ₦80 = ₦640.

 

WORKING EXAMPLE 2 – A trader buys 16 pairs of shorts at ₦4,000. How much will he pay for 35 pairs of shorts?

 

SOLUTION

Cost of 16 pairs of shorts is ₦4,000

Cost of 1 pair of short is ₦4,000/16 = ₦240.

Cost of 35 pairs of shorts is 35 x ₦240 = ₦8,750.

 

WORKING EXERCISE 

1. A girl saves ₦600 every five days, how much can she save in thirty days.

2. A lorry travels 60 km in 30 minutes. How long will it take to travel 180 km?

 

 

INDIRECT OR INVERSE PROPORTION 

Inversely Proportion, an increase in one quantity causes a decrease in another and vice versa.

For example,

20 men work for 6 days, 30 men work for 4 days, 40 men for 3 days and so on. As the number of men increasing, number of days decreasing.

 

WORKING EXAMPLE 1 – 35 workers can build a house in 16 days. How many days will it take 28 workers working at the same rate to build the same house?

 

SOLUTION

35 workers can build in 16 day,

1 worker can build in 35 x 16.

28 workers build in d – days,

1 worker can build in 28 x d.

Therefore, 35 x 16 = 28 x d

d = (35 x 16)/28 = 20

Now, 28 workers can be build in 20 days

 

WORKING EXAMPLE  – If 4 girls can weed a field in 10 days, how long will 5 girls take to weed it.

4 girls can weed a field in 10 days, 1 girl weed a field in 4 x 10 days.

5 girls cuts weed a field in d – days, 1 weed a field in (5 x d) days.

Therefore, 4 x 10 = 5 x d

d = (4 x 10)/5 = 8 days.

5 girls will take weed a farm in 8 days.

 

WORKING EXERCISE 

1. A man takes 5 minutes to drive 800 metres what distance can he drive in 16 minutes?

2. 40 pupils can eat a bag of rice in 8 days. How long will it last 16 children?