The term percent means per hundred, or hundredths. Percents are ratios that are often used to represent parts of a whole, where the whole is considered as having 100 parts.
1 percent means 1 part out of 100, or
50 percent means 50 parts out of 100, or
Note that the part is the numerator of the ration and the whole is the denominator. Percents are often written with the symbol, as follows.
To compute a percent, given the part and the whole, divide the part by the whole. The result will the decimal equivalent, so multiply the result by 100 to convert to percent.
Ex. What percent of 150 is 12.9?
Sol. Here the whole is 150 and the part is 12.9.
To find the part that is a certain percent of a whole, you can either multiply the whole by the decimal equivalent of the percent or set up a proportion to find the part.
Ex. To find 30% of 350, multiply 350 by the decimal equivalent of 30%, or 0.3, as follows.
To use a proportion, you need to find the number of parts of 350 that yields the same ratio as 30 out of 100 parts. You want a number that satisfies the proportion
Solve for yields so 30% of 350 is 105.
Given the percent and the part, you can calculate the whole. To do this you can either use the decimal equivalent of the percent or you can set up a proportion and solve it.
Ex. 15 is 60% of what number?
Sol. Use the decimal equivalent of 60%. Because 60% of some number is 15, multiply by the decimal equivalent of 60%, or 0.6.
Now solve for by dividing both sides of the equation by 0.6 as follows.
Although the discussion about percent so far assumes a context of a part and a whole, it is not necessary that the part be less than the whole. In general, the whole is called the base of the percent . When the numerator of a percent is greater than the base, the percent is greater than 100%. For e.g. 15 is 300% of 5, since
It is also not necessary for the part to be related to the whole at all, as in the question, "a teacher's salary is what percent of a banker's salary?".
When a quantity changes from an initial positive amount to another positive amount, for example, an employee's salary that is raised, you can compute the amount of change as a percentile of the initial amount. This is called percent change.
For e.g. if a quantity increases from 600 to 750, then the percent increase is found by dividing the amount of increase, 150 by the base, 600, which is the initial number given.
If a quantity decreases from 500 to 400, calculate the percent decrease as follows.
The quantity decreased by 20%.
When computing a percent increase, the base is the smaller number. When computing a percent decrease, the base is the larger number. In either case, the base is the initial number, before the change.
Ex. An investment in a mutual fund increased by 12% in a single day. If the value of the investment before the increase was $1,300, what was the value after the increase?
Sol. The percent increase is 12%. Therefore, the value of the increase is 12% of $1,300, or, using the decimal equivalent, the increase is (0.12)($1,300) = $156.
Thus, the value of the investment after the change is
$1,300 + $156 = $1,456
Because the final result is the sum of the initial investment , 100% of $1,300 and the increase, 12% of $1,300, the final result is 100% + 12% = 112% of $1,300.
Thus, another way to get the final result is to multiply the value of the investment by the decimal equivalent of 112% which is 1.12:
($1,300)(1.12) = $1,456
A quantity may have several successive percent changes. The base of each successive percent change is the result of the preceding percent change.
Ex. The monthly enrollment at a preschool decreased by 8% during one month and increased by 6% during the next month. What was the cumulative percentage change for the two months?
Sol. If E is the enrollment before the first month, then the enrollment as a result of 8% decrease can be found by multiplying the base E by the decimal equivalent of , which is 0.92:
The enrollment as a result of the second percent change, 6% increase, can be found by multiplying the new base 0.92E by the decimal equivalent of , which is 1.06:
The percent equivalent of 0.9752 is 97.52%, which is 2.48% less than 100%. Thus, the cumulative percent change in the enrollment for the two months is a 2.48% decrease.