Expressing One Quantity as Percentage of Another Number

In a school, 56 out of 70 teachers are female. What percentage of the teachers are females? What percentage of them is male? The fraction of female teachers in the school is 56/70 changing this fraction to percentage we have
\frac{{56}}{{70}} x 100% = 80%
80% of the teachers are female and percentage of male teachers (100%-80%) =20%
In general to express one quantity “a” as a percentage of the other quantity “b”, we have

  1. Write the fraction \frac{a}{b}
  2. Multiply fraction \frac{a}{b} by 100% to convert into percentage.

Example:
108 students out of 150 are passed in Math and 96 out of 160 are passed in English. Find percentage of passed students.
Solution:
Percentage of passed in Math = \frac{{108}}{{150}}x 100% = 72%
Percentage of passed in English = \frac{{96}}{{160}}x 100% = 60%

Finding a Percentage of a Number:
In order to find percentage (a\% ) of another number “b”. We have the following method.

  1. Multiply a\% with the number “b” i.e. b{\text{  x }}a\%
  2. Simplify it, if possible.

Example:
If 75% of the students in a class of 40 passed a Mathematics test. How many of them failed?
Solution:
Total Students = 40
Percentage of passed students = 75%
No. of students who passed the test = 75% of 40 students = \frac{{75}}{{100}}x  40 = 30
No. of failed students = 40 – 30 = 10

Example:
Find (1) 25% of 21.60 (2) 37\frac{1}{2}% x 1.60
Solution:

  1. 25% of 21.60 = \frac{{25}}{{100}}x 21.60 = 5.40
  2. 37\frac{1}{2}% x 1.60 = \frac{{75}}{2}% x 1.60 = \frac{{75}}{{2{\text{ x 100}}}}x \frac{{160}}{{100}}= = 0.60

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