Percentages | Mental Mathematics for Class 8 PDF Download

Introduction

• Hundredth Part: If you divide any thing into 100 equal parts, then each part would be known as hundredth part.
• Percentage: By a certain percentage, we mean “that many hundredth”
  We denote x  percentage by x , thus
  x% = x/100

Convert a Percentage into a Fraction

For converting a percentage into fraction, divide it by 100 and remove the % sign.
Thus x% = x/100
Example: 5% = 5/100 = 0.05

Convert Fraction into Percentage

For converting a fraction into a percentage, multiply the fraction by 100 and add %  sign to the resultant.

Example: 0.05 = (0.05 × 100) = 5%

Convert a Percentage into a Ratio

A percentage can be expressed as a ratio with the first term equal to the given percentage and the second term equal to 100
Therefore, x% = x/100
Example: 5% = 5/100 = 1/20

Convert Ratio into a Percentage

First write the ratio as a fraction and then multiply the fraction by 100 and put %  sign.

Example: 

Convert a Percentage into a Decimal

First convert the percentage into fraction and then convert fraction into a decimal.
Example: 75% = 75/100 = 0.75

Convert a Decimal into a Percentage

First convert the given decimal into a fraction and then multiply the fraction by 100  and add %  sign.
Example: 

Increasing or Decreasing a certain Quantity by a Certain Percentage

• If you have to increase a number a by x% , then the new number would be  
• If you have to decrease a number a by  x% , then the new number would be