Expressing One Quantity as a Percentage of Another Number

In a school, 56 out of 70 teachers are female. What percentage of the teachers is female? What percentage of them is male? The fraction of female teachers in the school is 56/70, so by changing this fraction to percentage we have

\frac{{56}}{{70}} x 100% = 80%

80% of the teachers are female and the percentage of male teachers (100%-80%) =20%

In general to express one quantity “a” as a percentage of the other quantity “b”, we:

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

Example:
108 students out of 150 passed math and 96 out of 160 passed English. Find the percentage of the students who passed.

Solution:
Percentage of students who passed math = \frac{{108}}{{150}}x 100% = 72%
Percentage of students who passed English = \frac{{96}}{{160}}x 100% = 60%

Finding the Percentage of a Number:

In order to find the percentage (a\% ) of another number “b”, we have the following method.

  1. Multiply a\% by “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 students who passed = 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