# FRACTIONS, RATIOS, DECIMALS AND PERCENTAGES

## 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%

Example 5.2

To change percentage to decimal fraction, simply divide by 100 and then convert to decimal fraction. E.g. convert 92% to decimal

Solution

92

100

920

900

200

200      =0.92

Example 5.3

1. Change the following to percentages

(a) 0.125    (b) 0.002

Solution

(a) 0.125×100% = 12.5%

(b) 0.002 = 0.002×100% = 0.2%

1. Change the following to decimal fractions

(A) 45 %    ( b) 8/3%

Solution

1. 45/100=0.45
2. 8/3= 8/3 ÷100/1= 8/3 x 1/100 = 8/300 = 4/150 = 2/75

0.02666

75        200

150

500

450

500

450

500

=0.0267

Class work

1. Change the following to percentage

(a) 0.264 (b) 0.875

1. Change the following to decimal fractions

(A) 60% (b) 52/3%

## APPLICATION OF DECIMAL FRACTIONS AND PERCENTAGES

Consider the following examples.

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

Solution

1. 15/100 of 2.8kg

15/100 x 2.8 x 1000g

15/100 x 2800

=420g

=420/1000

=0.420kg

1. b. 3.3/7.5 x 100/1

33/75 x 100/1

11×4 = 44%

1. 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=1000cm3)

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

## 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

1. 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

1. For 3 days =3 x 90 = 270
2. For 24 days = 24×90 = N 2,160
3. For x days =X x 90 = N 90 x

Inverse Proportion

Example

1. 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

1. 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

1. A woman is paid N 750 for 5 days, Find her pay for (a) 1 day (b) 22 days
2. 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
3. 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

1. 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

1. 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

1. 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

1. 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

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

## WEEKEND ASSIGNMENT

1. 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

1. A girl buys 7 pens for N How would ten pens cost? (a)#300(b)#30(c)#3(d)#200
2. Fill in the gap in m: a =16:24 (a) 10 (b) 12 (c) 4 (d) 6
3. Express 90km /hr: 120km /hr as simple as possible (a) 4:3 (b) 3:4 (c) 2:3 (d) 3:2
4. 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?