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