MATHEMATICS - FORM 1
CHAPTER 5
PERCENTAGE
PERCENTAGES
A) Expressing Percentages as the
Number of Parts in every 100
1. The symbol for percentage is %.
2. A percentage is a fraction in which the
denominator is 100.
For example :9 = 9%
100
32 = 32%
100
3. Convercely, percentages can be expressed
as fractions.
For example :24 = 24%
100
122 = 122%
100
Worked Example
Express each of the following as a percentage.
(a) 72
100
(b) 102
100
Solution
(a) 72 = 72%
100
(b) 102 = 102%
100
Worked Example
Convert the following to fraction with 100
as their denominators.
(a) 6%
(b) 75%
Solution
(a) 6% = 6
100
(b) 75% = 75
100
B) Changing a Fraction or Decimal to
a Percentage and vice versa
1. We can change a fraction or a decimal to
a percentage by multiplying it by 100.
Worked Example
Convert the following to percentages.
(a) 1
2
(b)
1
3
200
Solution
(a) 1 = 1 x 100
2 2
Worked Example
Convert each of the following to a fraction.
(a) 0. 6
(b) 1. 02
Solution
(a) 0. 6 = 0. 6 x 100%
= 60%
(b) 1. 02 = 1. 02 x 100%
= 102%
When converting a percentage to a fraction or a
decimal, first change the percentage to a fraction
with 100 as its denominator.
Worked Example
Convert each of the following to a fraction.
(a) 140%
Solution
Worked Example
Convert the following to decimals.
(a) 55%
(b) 324%
Solution
(a) 55% = 55
100
= 0.55
(b) 324% = 324
100
= 3. 24
COMPUTATIONS AND PROBLEM SOLVING
A) Finding the Percentage of a Quantity
Worked Example
Find
(a) 5 1 % of 600,
2
(b) 36% of 50 buttons,
(c) 120% of RM800.
Solution
B) Expressing One Number as a
Percentage of Another
In general, to express one number, y , as a
percentage of another number, z, we
(a) write y as a fraction of z,
(b) multiply the fraction y by 100% to convert
z
it to a percentage.
Worked Example
Find the percentage of the following.
(a) 8 of 10
(b) 50 sen of RM1
Solution
C) Finding a Number when given the percentage
Worked Example
Find the original value if 30% of the original
value is 12.
Solution
D) Finding Percentage of Increase or Decrease
Worked Example
Find the percentage of increase or decrease of
the following.
(a) 200 is increased by 50.
(b) 25 is decreased to 10.
Solution
E) Problem Solving
i - Finding the change in value and the final
value
1.To find the increase in value, use the
formula below :
2. To find the final value, use any one of the
formula below :
Worked Example
The population of a villlage was 2 000. It has
increased by 10% after 5 years. Find the new
population of the village.
Solution
1. Understand the problem
Given information :
Number of population = 2 000
Percentage of increase = 10%
Find : The new population
2. Devise a plan
Find the increase in population, then add
to the number of population.
3. Carry out the plan
Increase in population
= 10% of 2 000
= 200 people
Therefore, the new population of the village
is 2 200 people.
4. Check
3. To find the decrease in value, use the formula:
4. Use any of the following formula to find the final
value:
Worked Example
A vessel contained 80 liters of water. 30% of water
was used. Find
(a) the amount of water used,
(b) the amount of water left.
Solution
(a) Amount of water used
= 24 liters
4. Amount of water left
= 80 liters - 24 liters
= 56 liters
ii) Finding the original value when given the
percentage change and the final value
Worked Example
After a 20% decrease in mass, a boy weights 40
kg. Find his mass before the decrease.
Solution
1. Understand the problem
Given information :
Percentage of decrease = 20%
Final value = 40 kg
Find : The mass before the degrease
2. Devise a plan
Use the unitary method.
3. Carry out the plan
New mass is 80% of old mass = 40 kg
1% = 40 kg
80
= 50 kg
4. Check
Percentage of decrease
iii) Finding profit and loses
1. A profit occurs when the selling price
is higher than the cost price.
2. When the selling price is lower than the
cost price, a loss is incurred.
3. Profit and loss can be calculated by using
the following formula :
4. Use one of the following formula to find
the percentage of profit or percentage of
loss.
Worked Example
The profit made on the sale of a camera
is 12% of the cost price. If the cost price
is RM50, find the profit.
Solution
1. Understand the problem
Given information :
Percentage of profit = 12%
Cost price = RM50
Find : The profit
2. Devise a plan
Use profit formula.
3. Carry out the plan
Profit = Percentage of profit x Cost price
Therefore, the profit is RM6.
4. Check
Percentage of profit
5. The unitary method can be used to find
the cost price.
Worked Example
Adina sold his bicycle for RM270 at a loss
of 40%. Find the cost price of the bicycle.
Solution
60% of cost price = RM270
1%
= RM270
60
Therefore, the cost price of the bicycle is
RM450.
Check :
Selling price = 60% * RM450
iv) Finding simple interest
1. Simple interest ( I ) is the amount of money
earned on savings or to be paid on loans
with banks and finance companies at a fixed
rate ( R ) over a period of time ( T ), in years.
2. The money deposited or loaned is called the
principal ( P ).
3. Simple interest and the rate in percentage a
year are calculated as follows :
Worked Example
Puan Asniza took a bank loan RM8 000. If the
simple interest paid is RM1 280 for 2 years,
calculate the simple interest rate.
Solution
1. Understand the problem
Given information :
Principal = RM8 000
Simple interest = RM1 280
Time = 2 years
Find : The simple interest rate
2. Devise a plan
Use simple interest rate formula.
3. Carry out the plan
Simple interest rate
= Simple interest x 100%
Principal x Time
Therefore, the simple interest rate is 8% a year.
4. Check
4. The principal can be calculate by the formula :
Worked Example
Jacky put his money in a bank to earn a
simple interest at a rate of 81% a year.
2
How much money did he put in if he gets
an interest of RM765 in 3 years ?
Solution
Simple interest for 1 year
Check : Simple interest
v) Finding dividends
1. Dividend is a part of the profit that a
company gives to its shareholders.
2. Dividend and percentage of dividend
can be calculate by using the formulae:
Worked Example
A company pays 6% dividend. Find the dividend
Chong receives for a RM7 000 investment.
Solution
1. Understand the problem
Given information :
Percentage of dividend = 6%
Amount invested = RM7 000
Find : The dividend
2. Devise a plan
Use dividend formulae.
3. Carry out the plan
Dividend
Amount
= Percentage of dividend x
invested
Therefore, Chong receives a dividend of
RM420.
4. Check
Percentage of dividend
Worked Example
Kasim receives a dividend of RM5 500 on his
investment of RM50 000 in a company. Find
the percentage of dividend declared by the
company.
Solution
Percentage of dividend
=
Dividend __ x 100%
Amount invested
Therefore, the company gives a dividend of
11%.
vi) Calculating commissions
1. A commission is an earning paid to an agent
on his total sales of a product.
2. Commission and the percentage of commission
can be calculated by using the formilae :
Worked Example
As a salesman, Dewi gets a commission of 5%
on the sale value of a jewellery sold at price of
RM6 000. What is the commission she gets ?
Solution
1. Understand the problem
Given information :
Percentage of commission = 5%
Total sales value RM6 000
Find : The commission
2. Devise a plan
Use commission formulae.
3. Carry out the plan
Commission = Percentage of x Total sales
commission
value
Therefore, the commission she gets is RM300.
4. Check
Worked Example
Ah Wah received RM7 360 as commission for a
RM92 000 house he sold. What is the percentage
of his commission ?
Solution
Percentage of commission
=
Commission x 100%
Total sales value
vii) Calculating discount
1. Discount is the amount taken off from the
list price or the original price.
Discount = Original price - Selling price
2. The formulae for calculating discount and
the percentage of discount are as follows :
Worked Example
The original price of a television set is RM2 000.
It is sold for RM1 700 after a discount. Find the
percentage of discount given.
Solution
1. Understand the problem
Given information :
Original price = RM2 000
Selling price = RM1 700
Find : The persentage of discount
2. Devise a plan
Find the discount, then use percentage of
discount formulae.
3. Carry out the plan
Discount = Original price - Selling price
= RM2 000 - RM1 700
= RM300
percentage of discount
=
Discount x 100%
Original price
Therefore, the percentage of discount given
is 15%.
4. Check
Discount = 15% * RM2 000
Worked Example
Find the original price of a book if it is sold for
RM48 after a 40% discount.
Solution
Therefore, the original price of the book is RM80.
Worked Example
The original price of a handbag is RM245.
If a discount of 20% is given at a sale, find
the discount given in RM.
Solution
Discount
= Percentage of discount x Original price
Therefore, the discount is RM49.