For the very first Lesson on percent, see Lesson 4.
In this Lesson, we will answer the following:
|1.||Every statement of percent can be expressed verbally in what way?|
|"One number is some percent of another number."|
|____ is ____ % of ____.|
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."
|2.||What is a percent problem?|
|Given two of those numbers, to find the third.|
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:
|1. Amount = Base × Percent|
This is Rule 1. To find the Amount, multiply. There is also a rule for finding the Base and finding the Percent.
2. Base = Amount ÷ Percent
3. Percent = Amount ÷ Base
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.)
|3.||How do we use a calculator to solve a percent problem?|
|Apply one of the three rules.|
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 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.
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
On multiplying by 100, the answer is 400.
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.
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.
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:
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:
Example 6. $48.60 is what percent of $96.40?
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
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
The actual price was $78.
Equivalently, the calculation is
For problems of percent increase or decrease, see Lesson 31.
|Percent||=||Amount ÷ Base|
At this point, please "turn" the page and do some Problems.
Continue on to the next Lesson.
Please make a donation to keep TheMathPage online.
Even $1 will help.
Copyright © 2013 Lawrence Spector
Questions or comments?