# 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**

- identify the meaning of ratio and simply ratio in its lowest form;
- apply ratio to real – life situation;
- find the ratio of family size to their resources;
- express two populations in ratio;
- find the ratio of HIV/AIDS prevalence between sexes and states.

**Proportion**

- identify the meaning of direct proportion and solve problems involving direct proportion;
- 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:

- Source for related charts
- Flash charts
- Inverse proportion charts
- Inverse population charts.

**METHOD OF TEACHING**

- Explanation
- Discussion
- Demonstration
- Questions and answers

**REFERENCE MATERIALS**

- Scheme of Work
- 9 – Years Basic Education Curriculum
- New Method Mathematics Book 6
- Prime Mathematics Book 6
- All Relevant Material
- Online Information

**Related post – LCM, HCF, order of fractions, place value of decimal number, scheme of work – first term – second term – third term **

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**CONTENT OF THE LESSON**

**LESSON 1 – R****ATIOS **

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**

- What is the total number of fruits?
- What is the total number of strawberries?
- What is the total number of oranges?
- What is the ratio of oranges to strawberries?
- What is the ratio of strawberries to oranges?
- What is the ratio of oranges to total fruit?
- What is the ratio of strawberries to total fruit?

**FURTHER EXERCISE – Quantitative **

**Sample**

**12**: 16 = 3 : 4- 2 : 5 = 8 :
**20**

**QUESTIONS**

- ____ : 12 = 9 : 4
- 3 : 6 = 9 : ____
- 2 : ____ = 6 : 40
- 10 : 4 = ____ : 8
- 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

- 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?
- 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 **

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

- A man takes 5 minutes to drive 800 metres what distance can he drive in 16 minutes?
- 40 pupils can eat a bag of rice in 8 days. How long will it last 16 children?

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### FOR SMASE ASEI PDSI METHOD ON RATIO AND PROPORTION, RATIO OF FAMILY SIZE AND RESOURCES, RATIO OF TWO POPULATION, RATIO OF PREVALENCE Of HIV/AIDS BETWEEN TWO SEXES AND TWO STATES

**PRESENTATION**

- To deliver the lesson, the teacher adopts the following steps:

- To introduce the lesson, the teacher revises the previous lesson. Based on this, he/she asks the pupils some questions;
- Guides pupils to revise previous work done on ratios;
- Pupil’s Activities – Revise the previous work on ratios.
- Guides pupils to solve problems on population;
- Pupil’s Activities – Solve problems on ratios.
- Guides pupils to apply ratio to everyday life;
- Pupil’s Activities – Apply the application of ratios in everyday life.
- Guides pupils to solve quantitative problems related to ratios.
- Pupil’s Activities – Solve quantitative reasoning problem related to ratios.
- 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;
- Pupil’s Activities – Solve examples on direct proportion.
- Guides pupils to note that his saving is in direct proportion to the number of days;
- Pupil’s Activities – Note that the saving is in direct proportion to the number of days.
- Guides pupils to solve problems on quantitative reasoning involving direct proportion;
- Pupil’s Activities – Solve quantitative aptitude problems involving direct proportion.
- Guides pupils to solve problems on inverse proportions;
- Pupil’s Activities – Solve given problems in inverse proportion.
- Guides pupils to identify some activities that are inversely related;
- Pupil’s Activities – Identify some daily life activities that are inversely related.
- Guides pupils to solve problems on quantitative reasoning in inverse proportions.
- 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:**

- solve given problems on ratios;
- solve some quantitative reasoning problems on ratios;
- solve given problems on direct proportions;
- solve problem on quantitative aptitude involving direct proportion;
- solve given problems in inverse proportions;
- solve given problems in quantitative reasoning in inverse proportions.

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