1. Percent
The symbol for percent is %.
The fraction 1/100 is written for %
So, 50% is 50 × 1/100 = 50/100 = ½
2. Formulas on Percent Change:
1. Percent Increase is (amount of increase/initial number) × 100%
2. Percent Decrease is (amount of decrease/initial number) × 100%
3. Formulas on Percent Comparison:
1. Percent Greater (more) is (difference of the numbers)/(smaller number) × 100%
2. Percent Smaller (less) is (difference of the numbers)/(greater number) × 100%
4. Formulas on Percent (total) change during successive percent changes:
Note: In the following, + sign denotes increase, and – sign, decrease.
1. If a number N is increased first by x% and next by y%, then the total percent change is
(x + y + (x y/100))%
2. If a number N is decreased first by x% and increased next by y%, then the total percent change is
(- x + y – x y/100)%
3. If a number N is increased first by x% and decreased next by y%, then the total percent change is
(+x – y –xy/100)%
5. Formulas on Three important concepts on percents:
1. Consider a number N.
It is successively increased twice by x% each time.
Then, the total percent increase is > 2x%
2. Consider a Number N.
It is successively decreased twice by x% each time.
Then, the total percent decrease is < 2x%
3. Consider a Number N.
It is successively increased and decreased by x% each time.
Then, the final value is less than the original value.