Percentages and Fractions

Percentages and fractions are related to each other and can be converted from one form to the other. Let's see how to do that.

Converting a percentage to fraction

Example:

Following is a cookie box containing 100 assorted cookies of 4 different shapes:
  • 10% are heart-shaped cookies
  • 25% are round cookies
  • 30% are square-shaped cookies
  • 35% are star-shaped cookies



Let's change each of the above percentages to fraction.

Heart-shaped  =  10%
   =  10 out of 100
   =   10 1
10010
   =   1 
10
 1 
10th
 of the cookies are heart-shaped.

Or,

1 out of every 10 cookies in the cookie box is a heart-shaped cookie.


Round  =  25%
   =  25 out of 100
   =   25 1
1004
   =   1 
 4
 1 
 4th
 of the cookies are round.

Or,

1 out of every 4 cookies in the cookie box is a round cookie.


Square-shaped  =  30%
   =  30 out of 100
   =   30 
100
   =   3 
10
 3 
10th
 of the cookies are square-shaped.

Or,

3 out of every 10 cookies in the cookie box are square-shaped cookies.


Star-shaped  =  35%
   =  35 out of 100
   =   35 7
10020
   =   7 
20
 7 
20th
 of the cookies are star-shaped.

Or,

7 out of every 20 cookies in the cookie box are star-shaped cookies.


Converting a fraction to percentage

Example:

Following is a cookie box containing 100 assorted cookies of 4 different shapes:
  •  
 1 
10th
 of the cookies are heart-shaped cookies
  •  
 1 
 4th
 of the cookies are round cookies
  •  
 3 
10th
 of the cookies are square-shaped cookies
  •  
 7 
20th
 of the cookies are star-shaped cookies



Let's change each of the above fractions to percentage. There are 3 different methods that you can use to do this.

Heart-shaped  =   1 
10
  (using Method 1)
   =   1 × 10 
10 × 10
  (change denominator to 100)
   =   10 
100
   =  10%
10 out of the 100 cookies in the cookie box are heart-shaped cookies.

Or,

10% of the cookies are heart-shaped cookies.


Round  =   1 
 4
  (using Method 1)
   =   1 × 25 
 4 × 25
  (change denominator to 100)
   =   25 
100
   =  25%
25 out of the 100 cookies in the cookie box are round cookies.

Or,

25% of the cookies are round cookies.


Square-shaped  =   3 
10
of 1 whole box   (using Method 2)
   =   3 
101
 × 10010%    (1 whole = 100%)
   =  30%
30% of the cookies are square-shaped cookies.


Star-shaped  =   7 
20
of 1 whole box   (using Method 3)
   =  7÷20 of 1 whole box
   =  0.35 of 1 whole box
   =  0.35× 100%    (1 whole box = 100%)
   =  35%
35% of the cookies are star-shaped cookies.