Lesson 13

PERCENT
WITH A CALCULATOR

For the very first Lesson on percent, see Lesson 3.

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 3) 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 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

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.

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.

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, without the division key, 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 11, we saw how to round off a decimal.  The following examples will require that.

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 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

On the screen, see

The actual price was $78.

*

For problems of percent increase or decrease, see Lesson 30.

At this point, please "turn" the page and do some Problems.

or

Continue on to the next Lesson.

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