Maths Form 1 Chapter 5 Percentages

   
 
 
 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           (b) 1  3  
     2                   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. 24COMPUTATIONS 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.