8 is 50% of 16.
Every statement of percent therefore involves three numbers. 8 is called the Amount. 50% is the Percent. 16 is called the Base. The Base always follows "of."
Example. "$78 is 12% of how much?" Which number is unknown -- the Amount, the Percent, or the Base?
Answer. We do not know the Base, the number that follows "of."
We have seen that to find
8% of $600,
for example, we multiply. (Lesson 3.) We can now recognize that $600 is the Base -- it follows "of," and 8% is the Percent. We are looking for the Amount. We can state the rule as follows:
This is Rule 1. To find the Amount, multiply. There is also a rule for finding the Base and finding the Percent.
Notice that we multiply only to find the Amount. In the other two cases, we divide.
(This follows from the relationship between multiplication and division, which we saw in Lesson 10.)
Example 1. How much is 37.5% of $48.72?
Solution. We have the Percent, and we have the Base -- it follows "of." We are missing the Amount. Apply Rule 1: Multiply
Base × Percent
Press the percent key % last. And when you press the percent key, do not press = . (At any rate, that is true for simple calculators.)
The answer is displayed:
If your calculator does not have a percent key, then express the percent as a decimal (Lesson 3), and press = . Press
Example 2. $250 is 62.5% of how much?
Solution. The Base -- the number that follows "of" is unknown. Apply Rule 2: Divide
Amount ÷ Percent
Do not press = . The answer is displayed:
Example 3. $51.03 is what percent of $405?
Solution. The Percent is unknown. Apply Rule 3:
Amount ÷ Base
$51.03 is 12.6% of $405.
Without a % key, press = .
Then move the decimal point two places right.
Again, we multiply in only one of the three cases; namely, to find the Amount.
In Lesson 11, we saw how to round off a decimal. The following examples will require that.
Example 4. How much is 9.7% of $84.60?
Solution. The Amount is missing. Multiply
Base × Percent.
It is not necessary to press the 0 of 84.60.
On the screen, see this:
Since this is money, we must round off to two decimal places. In the third place is a 6; therefore add 1 to the second decimal place:
Example 5. $84.60 is 9.7% of how much? (Compare this with Example 4.)
Solution. Here, the Base is missing. Divide:
On the screen, see
Again, this is money, so we must approximate it to two decimal places:
Example 6. $48.60 is what percent of $96.40?
Solution. The Percent is missing. Divide:
Percent = Amount ÷ Base.
Again, it is not necessary to press the 0's on the end of decimals.
On the screen, see this decimal:
Let us round this off to one decimal place. Since the digit in the second place is 1 (less than 5), we have
At this point, please "turn" the page and do some Problems.
Continue on to the next Lesson.