Lesson 14 PERCENT




For example, 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 (Lesson 4) that to find 8% of $600, for example, we multiply. 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 11.) 



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
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 4), 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. Press
Do not press = . The answer is displayed:
Now, for calculators that instead of a division key ÷ have the division slash / , the percent key % will not be effective in finding the Base or the Percent. To find the Base, do not press the percent key. Press equals = . Then multiply by 100. Again, $250 is 62.5% of how much? Press
See:
On multiplying by 100, the answer is 400. Or, change 62.5% to the decimal .625 (Lesson 4), and press
See:
Example 3. $51.03 is what percent of $405? Solution. The Percent is unknown. Apply Rule 3: Amount ÷ Base. Press
See
$51.03 is 12.6% of $405. For calculators without a % key, press = .
Similarly, with only the division slash, press = .
In either case, see
Then multiply by 100 by moving the decimal point two places right. Again, we multiply in only one of the three problems; namely, to find the Amount. Now in Lesson 12, 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. Press
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 digits. In the third decimal place is a 6; therefore add 1 to the second place: $8.21 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 digits: $872.16 Example 6. $48.60 is what percent of $96.40? Solution. The Percent is missing. (Compare Example 3.) 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 digit. Since the digit in the second place is 1 (less than 5), this is approximately 50.4%. Example 7. Michelle paid $82.68 for a pair of shoes  but that included a tax of 6%. What was the actual price of the shoes before the tax? Solution. The actual price, the base, was 100%. When the 6% tax was added, the price became 106% of that base. So the question is: $82.68 is 106% of how much? To find the Base, press
See
The actual price was $78. Equivalently, the calculation is
* For problems of percent increase or decrease, see Lesson 31.
At this point, please "turn" the page and do some Problems. or Continue on to the next Lesson. Introduction  Home  Table of Contents Please make a donation to keep TheMathPage online. Copyright © 2016 Lawrence Spector Questions or comments? Email: themathpage@nyc.rr.com 