- Fractions and Percentages
- Proportion
- Ratio
- Rate

**Fractions and percentages**

A fraction can be converted to decimal by dividing the numerator by its denominator. It can be changed to percentage by simply multiplying by 100.

**Example 5.1**

- Change 3/8 into a decimal and percentage
- Convert 0.145 to percentage

**Solution**

1) 3/8 = 0.375 in decimal

3/8 x 100% = 37.5%

2) 0.145×100=14.5%

**APPLICATION OF DECIMAL FRACTIONS AND PERCENTAGES**

Consider the following examples.

- Find 15% of 2.8kg
- Express 3.3 mass a percentage of 7.5
- Find 331/3 % of8.16litres

**Solution**

**a.** 15/100 of 2.8kg

15/100 x 2.8 x 1000g

15/100 x 2800

=420g

=420/1000

=0.420kg

** b**. 3.3/7.5 x 100/1

33/75 x 100/1

11×4 = 44%

** c**. 331/3% of 8.16litres

100/3 of 8.16litres

100/3 of 8.16litres

100/3 x 8.16litres

100/3 x 8.16 x 1000 (1litre=1000cm^{3)}

100/3 x 8160

100/3 ÷100/1 x 8160

100/3 x 1/100 x 8160

=2700/1000= **2.720litres**

**Class work**

1. Express1.5 as a percentage of 2.5 m

2. Find 662/3 % of2.4m

**READING ASSIGNMENT**

New General Mathematics, UBE Edition, chapter 1 Pages 78-79

Essential Mathematics by A J S Oluwasanmi, Chapter 1 pages 61-64

**Proportion**

Proportion can be solved either by unitary method or inverse method. When solving by unitary method, always

- write in sentence the quantity to be found at the end.
- decide whether the problem is either an example of direct or inverse method
- find the rate for one unit before answering the problem.

**Examples**

- A worker gets
~~N~~900 for 10 days of work, find the amount for (a) 3 days (b) 24 days (c) x days

**Solution**

For 1 day = ~~N~~ 900

1 day = 900/10 = N90

a. For 3 days =3 x 90 = 270

b. For 24 days = 24×90 = ~~N~~ 2,160

c. For x days =X x 90 = ~~N~~ 90 x

**Inverse Proportion**

Example

- Seven workers dig a piece of ground in 10 days. How long will five workers take?

**Solution**

For 7 workers =10 days

For 1 worker =7×10=70 days

For 5 workers=70/5 =14 days

- 5 people took 8 days to plant 1,200 trees, How long will it take 10 people to plant the same number of trees

**Solution**

For 5 people =8 days

For 1 person =8×5=40 days

For 10 people =40/10 =4 days

**Class Work**

- A woman is paid
~~N~~750 for 5 days, Find her pay for (a) 1 day (b) 22 days - A piece of land has enough grass to feed 15 cows for x days. How long will it last (a) 1 cow (b) y cows
- A bag of rice feeds 15 students for 7 days .How long would the same bag feed 10 students

Note on direct proportion: this is an example of direct proportion .The less time worked (3 days) the less money paid (#270) the more time worked (24 days) the more money paid (~~N~~ ~~N~~ 2,160)

**Ratio**

Ratio behaves the same way as fraction. Ratios are often used when sharing quantities..

**Example**

600/800=600/800=3/4

300-400=600-800=1200-1600=3=4

**Example**

1. Express the ratio of 96 c: 120c as simple as possible

Solution 96c: 120c=96/120=4/5=4.5

2. Fill in the gap in the ratio of 2:7=28

**Solution** let the gap be X

2/7 = X/28

7X =2 x 28

X=2 x 28/7

X=2 x 4

X = 8

- Two students shared 36 mangoes in the ratio 2:3 How many mangoes does each student get?

**Solution**

Total ratio =2+3=5

First share=2/5×35/1=21 mangoes

**Rate**

Rate is the change in one quantity to the other. Examples are 45km/hr, a km, 1 litre etc

Worked examples

- A car goes 160 km in 2 hrs what is the rate in km/hr?

**Solution**

In 2 hrs the car travels 160 km

In 1 hr the car travels 160/2=80km

Therefore the rate of the car is 80km/hr

- A car uses 10 litres of petrol to travel 74 km. Express its petrol consumption as a rate in km per litre.

**Solution**

10 litres =74 km

1 litres = 74/10 km

=7.4 km

**Class work**

- A car factory made 375 cars in 5 days, Find its rate in cars per day.
- A car travels 126 km in 11/2 hrs. Find the rate in km per hr.

**READING ASSIGNMENT**

New General Mathematics, UBE Edition, Chapter 1, pages 80-85

Essential Mathematics by A J S Oluwasanmi, Chapter 1, pages 69-72

**WEEKEND ASSIGNMENT**

- 5 men build in 10 days, how long would it take 25 men?

(a) 3 days (b) 2 days (c) 5 days (d) 10 days

- A girl buys 7 pens for
~~N~~210. How would ten pens cost? (a)#300(b)#30(c)#3(d)#200 - Fill in the gap in m: a =16:24 (a) 10 (b) 12 (c) 4 (d) 6
- Express 90km /hr: 120km /hr as simple as possible (a) 4:3 (b) 3:4 (c) 2:3 (d) 3:2
- A factory makes
~~N~~2000 pencils in 10 days, Find its production rate of pencils per day (a)~~N~~20 per day (b)~~N~~100 per day(c)~~N~~50 per day (d)~~N~~200 per day

**THEORY**

1. Find 50% of 3.5m

2. A bag of corn can feed 100 chicks for 12 days. How long would the same bag feed 80

chickens?