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

100

920

900

200

200 =0.92

Example 5.3

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%

Change the following to decimal fractions

(A) 45 % ( b) 8/3%

Solution

45/100=0.45
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

Change the following to percentage

(a) 0.264 (b) 0.875

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

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 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

Express1.5 as a percentage of 2.5 m
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

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

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

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

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

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.

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 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