WEEK 6&7

SUBJECT: MATHEMATICS

TERM: 1^ST TERM

CLASS: PRIMARY 6

TOPIC: RATIO AND PROPORTION

4. A paint mix uses red and white in the ratio 3: 10. 6 3/5 liters of red paint are used. How much white paint is used?
5. A necklace has silver and blue beads in the ratio 2 : 3. There are 24 silver beads on the necklace. How many blue beads are there?
6. In a school gathering, the ratio of boys to girls was 4 : 5. There were 32 boys.
7. a) How many are girls? b) How many people were there altogether?
8. c) What is the ratio of i) girls to boys? ii) girls to total people?
9. 2 000 is shared in the ratio 7: 3 between Faka and Osarentin. How much does each receive?
10. 2 kg of flour is shared in the ratio 4: 6 between Ololade and Chingere. How much does each receive?
11. The ratio of Mr Umoh’s new salary to his old salary was 4: 3. If his old salary was #57 000, what is his new salary?
12. 70 liters of petrol was shared in the ratio 1: 2: 4 among three drivers. How many liters of petrol will each driver receive?
13. Vanilla milk shake is made by mixing milk and flavoring in the ratio of 14:1. How much milk and flavoring is needed to make 3 liters of milk shake?
14. The ratio of the weight of Inyang and Onome is 5: 3. The lighter person weighs 48 kg.
15. a) What does the heavier person weigh? b) Who is the heavier person?
16. c) What is their total weight?
17. Mr and Mrs. Shuaibu bought some shares for their three children Jumai, Danladi and Kabiru in the ratio 7: 5: 3. If the total shares bought were 90000 units, how many units did each receive?
18. Profits from a business are shared among Hakeem, Gafar and Eniola in the ratio 7: 2: 3.
19. What fraction of the profit does each person get?
20. If the profit shared was 7 350 000, find out how much each person gets.

Ratio and population issues

Examples

In Delta State, the money allocated to health care in one of its local government areas with a population of 96 000 people is 192 000 000. Here the ratio in naira per citizen is worked out. Solution

000: 192 000 000

000: 192 000 000

96: 192 000 (divide by 1 000)

1: 2 000 (divide by 96)

1: 2 000

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Exercise 2

The money allocated for health care from Lagos State Government to some of the local areas is listed below. Work out the ratio in naira per citizen. (Figures are not actual.) LGA Population Money allocated ()

1. Ikeja 72 000 144 000 000
2. Mushin 45 000 97 000 000
3. Alimosho 30 000 65 000 000
4. Epe 28 000 60 000000
5. Shomolu 65 000 180 000 000

Examples

All the children in a community of 66 families add up to 110 children. Study how to calculate the ratio of children per family.

Ratio of children per family

66 families:                             families: 10 children

families: 5 children

family: 1.6 children

1: 2

Exercise 3

Find the ratio of the number of children to the number of families in the different communities below. Round up to the nearest whole number.

Community Number of families Number of children

1. Otu 53 123
2. Epe 38 120
3. Ajaji 64 185
4. Ute 110 328
5. Nkpitime 96 272
6. The total number of children in a village of 20 families is 125. Calculate the ratio of children per family.

Birth rate: The number of births every year for every 1 000 people in the population of a place.

Fertility rate: The number of children born per woman in a population. Death rate: The number of deaths every year for every 1 000 people in the population of a place.

Infant mortality: The number of deaths of babies at birth or just after birth per 1 000 live-births in the population of a place.

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Examples

2 800 children were born in a Nigerian city with a population of 250 000. Here the birth rate is calculated. Ratio of population to number of births

                        250

11.2

Therefore, the birth rate is 11 births/1 000.

If 1 820 children were born by all the women in town numbering 910, find the fertility rate. Study this answer. Ratio of the number of women to the number of children born

=910: 1 820

1: 2

Therefore, fertility rate is 2 children/woman.

1 890 people died in a year in a town with a population of 63 000. Here the death rate is calculated. Ratio of number of people to number of deaths

=63 000: 1 890

=1 000: 1890

                  63

=1 000: 30

Therefore, the death rate is 30 deaths/1 000.

Exercise 4

1. In a new capital city established by a government, the population was 32000. If the total number of children born that year was 672, what was the birth rate?
2. If 1 845 children were born by all the women numbering 315 in a community, find the fertility rate.
3. A total of 2 002 deaths were recorded in a community with a population of 154 000. Calculate the death rate.
4. A total of 50 infant deaths were recorded among 500 live-births in a local government area. Calculate the infant mortality rate.
5. Find the total number of deaths in a city with a population 80 000, if the death rate is 13/1 000.

Examples

The number of infant deaths recorded among 78 000 live-births in a constituency was 1 560. Here the infant mortality rate has been calculated. The ratio of the number of live-births to the number of infant deaths

=78 000: 1 560

=1 000: 1560

                   78

=1 000: 20

Therefore, the infant mortality rate is 20 deaths/1 000 live-births

In a year, the death rate recorded in a village with a population of 80 000 was 12 deaths/1 000. Here the total number of deaths in that year has been calculated.

Ratio of death rate

=1 000: 12 deaths

=80 000: 12 × 80

=80 000: 960 deaths

Therefore, number of deaths =960

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Exercise 5

1. If 1 845 children were born in a year in a city with a population of 123 000, calculate the birth rate.
2. If 1 890 children were born by all the women totaling 135 in a village, what is the fertility rate?
3. Assume that 2 448 people died in a year in a local government area with a population of 136 000. Find the death rate.
4. A total number of 6 364 children were born in a year in a village with a population of 172. Calculate the birth rate.
5. Work out the number of deaths in a camp with a population of 672 000 if the death rate was 32 deaths per 1 000.
6. The fertility rate in a settlement was 6 children born per woman. Calculate the number of children born by all the 1 792 women in the settlement.

PROPORTION

Study these statements:

The cost of 1 pencil is 10.00

Then the cost of 4 pencils is 40.00

Likewise the cost of 12 pencils is 120.00

As the number of pencils increases the cost also increases. The ratio of number of

We say, proportion is an equation showing when two ratios are equal.

For example, 1/10=4/40

Since 1: 10 =4: 40

We can then say that the cost of the pencils is in direct proportion to the number of pencils.

Examples

1. The cost of five pairs of shorts is 1 340. Find the cost of eight pairs. These workings show how this word problem is solved.

Solution

5 pairs of shorts cost #1 340

1 pair of shorts costs #1 340/5 [Divide N1 340 by 5]

                                 =268

8 pairs of shorts will cost #268 ×8 [Multiply the cost of one pair by 8]

=#2 144

Direct proportion

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2. The cost of petrol is #97.00 per liter.

What is the cost of 5 liters? How many liters do I get for 1 455.00?

Solution

1 liter of petrol costs #97.00

5 liters of petrol will cost #97 ×8 =485.00 #97.00 is the cost of 1 liter of petrol.

#1 455.00 will be the cost of1/97×1455/1 liters of petrol =15 liters of petrol.

3. The following solutions work out costs if a kilogram of apples cost N600.00.

Weight, W (kg) 0        1        2       3        4

Cost, C (Naira)          600

Solution

1 kg of apples costs =#600

3 kg of apples will cost =#600 ×3

              =#1 800

• kg of apples costs -#600
• kg of apples will cost =#600 ×2

                     =#1 200

1 kg of apples costs =#600

4 kg of apples will cost =#600 ×4

                          =2 400

The table is

Weight, W (kg) 0 1 2 3 4

Cost, C (Naira) 0 600 1200 1800 2400

The cost is directly proportional to the weight of apples.

Exercise

1. Find the cost of 24 oranges, if 3 oranges cost 80.00?
2. If eight oranges cost 200, find the cost of twenty oranges.
3. A car travels 60 km in 1

2 hour. How long will it take to travel 180 km?

4. A trader buys 16 pairs of shorts at 4 000. How much will he pay for 35 pairs of shorts?
5. If 10 crates of eggs cost 5 400, how much will 500 eggs cost?

eggs)

6. An American changed 120 dollars for 15 600. How much in naira will he get for 45 dollars?
7. 54 apples cost 3 240. Find the cost of 45 apples.
8. A boy takes 5 minutes to cycle 800 metres, what distance can he cycle in 8 minutes?
9. If 1 liter of petrol is needed for a car to travel 18 km, how far can the car travel on 15 liters of petrol?
10. A boy saves 300 every five days, how much can he save in 20 days?

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 Indirect proportion Study the table below.

Number of girls to scrub   1     2     3     4       5      6

Time taken (mins)             60    30    20   145 12   10

The above table shows the number of girls that can scrub a room and the time that it will take to complete the work.

You will observe that as the number of girls increases the time taken to complete the work decreases, in the same way. The product of the number of girls that scrub and the time taken are all equal.

That is: 1×60 =2 ×30 =3 ×20 4 ×15 =5 ×12= 6 ×10.

This type of proportion is called inverse proportion or indirect proportion.

Examples

If 10 girls are to scrub the room, how many minutes will it take them? Study the solution to this word problem.

Solution

Number of girls ×time taken =60

                        10×time taken =60

                          Time taken =60

                                                    10

                                       =6 minutes

If 15 laborers can load a ship in 10 days, how many extra laborers  must be employed to load the ship in 6 days? Study the solution.

Solution

Method 1

Product of 15 laborers and 10 days =15 ×10 =150

Thus 6 days ×the laborers =150

The laborers =150/6=25

The extra laborers to be employed = 25 – 15 =10

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Method 2

In 10 days, the laborers to load the ship =5

In 1 day, the laborers to load the ship will be =15 ×10

In 6 days, the laborers to load the ship will be =15× 10/6

                                                                                        25

Thus the extra laborers to be employed 25 – 15 =10

Examples

Twelve men can weed a farm in 6 days. How many men can weed it in 8 days if they are working at the same rate? Study the following solution to this word problem.

Solution

The required answer is in terms of men, so the statement is thus.

In 6 days the farm is completely weeded by 12 men.

In 1 day the farm will be completely weeded by 12 ×6 men.

(In 1 day more men would have to weed the farm)

In 8 days the farm will be completely weeded by 12× 6/8men =9 men.  Exercise

1. A farmer has enough hay to feed 9 horses for 10 days. How long will the same supply of hay feed 6 horses?
2. If 24 workers can build a jetty in 15 weeks, how many workers will build the Jetty in 12 weeks if they are working at the same rate?
3. When a packet of chewing gums is shared among 30 children, each child gets 8 chewing gums. How many chewing gums will each child get if the packet is shared among 40 children?
4. A driver travels 80 km/h and completes a journey in 3 hours. How long will it take to complete the same journey if the speed is 120 km/h?
5. A fence can be built by 10 men in 7 days. If the fence is to be completed in 5 days, how many a) men are required in total? b) More men are required? 6. 40 children can eat a bag of rice in 8 days. How long will it last 5 children?
6. A plantation of palm fruits can be harvested by 20 men in 10 weeks. Each man harvests a fixed weight of palm fruits in 1 week. Find how many men can harvest the palm fruit in: a) 8 weeks b) 5 weeks.