# Ratio and Proportion

Last Updated on October 15, 2018 by Alabi M. S.

MATHEMATICS

FIRST TERM

SIXTH WEEK

BASIC 6

THEME: NUMBER AND NUMERATION

TOPIC: Ratio and Proportion

PERFORMANCE OBJECTIVES

By the end of the lesson, the pupils should have attained the following objectives (cognitive, affective and psychomotor) and be able to:

• Ratio
1. identify the meaning of ratio and simply ratio in its lowest form;
2. apply ratio to real – life situation;
3. find the ratio of family size to their resources;
4. express two populations in ratio;
5. find the ratio of HIV/AIDS prevalence between sexes and states.
• Proportion
1. identify the meaning of direct proportion and solve problems involving direct proportion;
2. identify indirect proportion.

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ENTRY BEHAVIOR

The pupils are required to already have learned fractions and decimals.

INSTRUCTIONAL MATERIALS

The teacher will teach the lesson with the aid of:

1. Source for related charts
2. Flash charts
3. Inverse proportion charts
4. Inverse population charts.

METHOD OF TEACHING

1. Explanation
2. Discussion
3. Demonstration

REFERENCE MATERIALS

1. Scheme of Work
2. 9 – Years Basic Education Curriculum
3. New Method Mathematics Book 6
4. Prime Mathematics Book 6
5. All Relevant Material
6. Online Information

Related post – LCM, HCF, order of fractions, place value of decimal number, scheme of workfirst termsecond termthird term

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CONTENT OF THE LESSON

### LESSON 1 – RATIOS

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.

Or we can use the word ” to “: 12 to 8.

Or write it like a fraction: 12/8.

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.

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WORK TO Do

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
1. 12 : 16 = 3 : 4
2. 2 : 5 = 8 : 20

QUESTIONS

1. ____ : 12 = 9 : 4
2. 3 : 6 = 9 : ____
3. 2 : ____ = 6 : 40
4. 10 : 4 = ____ : 8
5. 1 : ____ = 6 : 24

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### LESSON TWO – APPLICATION OF RATIO TO REAL LIFE SITUATION

• Problems solving involving ratio

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.

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.

WORK TO DO – I can do it too.

• Solve the following word problems
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?

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### LESSON 3 – RATIO OF 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.

• Problems solving involving ratio

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 : ₦4,800 = 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.

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### POPULATION AND ALLOCATION

• Problems solving involving ratio

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.

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

• Problems solving involving ratio

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.

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### PROPORTION

Proportion means equal in two ratio.

### LESSON 4 – DIRECT PROPORTION

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

• Problems solving involving ratio

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[mediator_tech]
• 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.

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.

WORK TO DO

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?

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### 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.

• Problems solving involving ratio

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.

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. [mediator_tech]

WORK TO DO

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?

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### PRESENTATION

• To deliver the lesson, the teacher adopts the following steps:
1. To introduce the lesson, the teacher revises the previous lesson. Based on this, he/she asks the pupils some questions;
2. Guides pupils to revise previous work done on ratios;
3. Pupil’s Activities – Revise the previous work on ratios.
4. Guides pupils to solve problems on population;
5. Pupil’s Activities – Solve problems on ratios.
6. Guides pupils to apply ratio to everyday life;
7. Pupil’s Activities – Apply the application of ratios in everyday life.
8. Guides pupils to solve quantitative problems related to ratios.
9. Pupil’s Activities – Solve quantitative reasoning problem related to ratios.
10. Guides pupils to solve direct proportion problems e.g. A man saves money everyday. If he saves ₦30 each day, how much can be saved in 4 days? He saves ₦120 in 4 days;
11. Pupil’s Activities – Solve examples on direct proportion.
12. Guides pupils to note that his saving is in direct proportion to the number of days;
13. Pupil’s Activities – Note that the saving is in direct proportion to the number of days.
14. Guides pupils to solve problems on quantitative reasoning involving direct proportion;
15. Pupil’s Activities – Solve quantitative aptitude problems involving direct proportion.
16. Guides pupils to solve problems on inverse proportions;
17. Pupil’s Activities – Solve given problems in inverse proportion.
18. Guides pupils to identify some activities that are inversely related;
19. Pupil’s Activities – Identify some daily life activities that are inversely related.
20. Guides pupils to solve problems on quantitative reasoning in inverse proportions.
21. Pupil’s Activities – Solve problems on quantitative reasoning in inverse proportion.

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CONCLUSION

• To conclude the lesson for the week, the teacher revises the entire lesson and links it to the following week’s lesson – ratio, percentage and population issues.

LESSON EVALUATION

Pupils to:

1. solve given problems on ratios;
2. solve some quantitative reasoning problems on ratios;
3. solve given problems on direct proportions;
4. solve problem on quantitative aptitude involving direct proportion;
5. solve given problems in inverse proportions;
6. solve given problems in quantitative reasoning in inverse proportions.

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