PERCENTAGE

PERCENTAGE

In this unit we shall look at the meaning of percentages and carry out calculations involving
percentages. We will also look at the use of the percentage button on calculators.
• calculate a percentage of a given quantity;
• increase or decrease a quantity by a given percentage;
• find the original value of a quantity when it has been increased or decreased by a given
  percentage;
• express one quantity as a percentage of another.

                                         CONTENT

1. Introduction 

2. Finding the original amount before a percentage change
3. Calculating percentages using a calculator 
4. Process to convert fraction into percentage and vice-versa.

1.INTRODUCTION

The word ‘percentage’ is very familiar to us as it is used regularly in the media to describe anything from changes in the interest rate, to the number of people taking holidays abroad, to the success rate of the latest medical procedures or exam results. Percentages are a useful way of making comparisons, apart from being used to calculate the many taxes that we pay such as VAT, income tax, domestic fuel tax and insurance tax.

Let us look at some common percentage amounts, and their fraction and decimal equiva-
lents.

                                 
                       

Expressing a change as a percentage

We might wish to calculate the percentage by which something has increased or decreased. To

do this we use the rule actual increase or decrease

original cost × 100% .So you write the amount of change as a fraction of the original amount, and then turn it into a

percentage.

Example :

A car cost rs12,000. After 3 years it is worth rs8,000.what is the percentage decrease?

solution

                                                         

                               

   

2. Finding the original amount before a percentage change

Example

A shop has reduced the cost of a coat by 15% in a sale, so that the sale price is £127.50. What was the original cost of the coat?

solution

If A is greater than B by 20% then by what % B is lesser than A?

solution

                             

Due to dccrease in rate of apples a man buys 3 apples for rs 1 instead of rs1.25.Find the decrease in rate of apples?

solution

3.Calculating percentages using a calculator

Here is a warning about using the percentage button on a calculator: the result depends on when you press the % button in your calculation. Sometimes it has no effect, sometimes it seems to divide by 100, and at other times it multiplies by 100. Here are some examples

• Pressing 48÷400% gives an answer of 12. Now 48÷400 = 0.12, so pressing the % button has had the effect of multiplying by 100. This has found 48 as a percentage of 400.

• Pressing 1 ÷ 2 × 300% gives the answer 1.5. Now 1 ÷ 2 × 300 = 150, so pressing the %button here has divided by 100. This has found 300% of a half.

• Pressing 400 × 50% gives an answer of 200. Now 400 × 50 = 20, 000, so pressing % here has divided by 100. This has found 50% of 400.

• Pressing 50% × 400 results in 400 on the display, requiring = to be pressed to display an answer of 20,000. So pressing the % button here has had no effect.

4. Process to convert fraction into percentage and vice-versa.

Here is the chart for you.