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
 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.

 Find 15% of 2.8kg
 Express 3.3 mass a percentage of 7.5
 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 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
 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
300400=600800=12001600=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
THEORY
 Find 50% of 3.5m
 A bag of corn can feed 100 chicks for 12 days. How long would the same bag feed 80 chickens?
See also
H.C.F & L.C.M AND PERFECT SQUARES