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:
- Write the fraction $$\frac{a}{b}$$
- 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.
- Multiply $$a\% $$ by “$$b$$”, i.e. $$b{\text{ x }}a\% $$
- 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:
-
25% of 21.60 = $$\frac{{25}}{{100}}$$x 21.60 = 5.40
- $$37\frac{1}{2}$$% x 1.60 = $$\frac{{75}}{2}$$% x 1.60 = $$\frac{{75}}{{2{\text{ x 100}}}}$$x $$\frac{{160}}{{100}}$$= = 0.60