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Lesson 13

# PERCENTWITH A CALCULATOR

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

In this Lesson, we will answer the following:

1. Every statement of percent can be expressed verbally in what way?
2. What is a percent problem?
3. How do we use a calculator to solve a percent problem?

 1. Every statement of percent can be expressed verbally in what way? "One number is some percent of another number." ____ is ____ % of ____.

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."

 2. What is a percent problem? Given two of those numbers, to find the third.

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:

 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.

 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

 4 8 . 7 2 × 3 7 . 5 %

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:

 18.27

If your calculator does not have a percent key, then express the percent as a decimal (Lesson 3), and press = .   Press

 4 8 . 7 2 × . 3 7 5 =

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

 2 5 0 ÷ 6 2 . 5 %

Do not press = .  The answer is displayed:

 400

Example 3.   \$51.03 is what percent of \$405?

Solution.  The Percent is unknown.  Apply Rule 3:

Amount ÷ Base

Press

 5 1 . 0 3 ÷ 4 0 5 %

See

 12.6

\$51.03 is 12.6% of \$405.

Without a % key, press = .

 5 1 . 0 3 ÷ 4 0 5 =

See

 0.126

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.

Press

 8 4 . 6 × 9 . 7 %

It is not necessary to press the 0 of 84.60.

On the screen, see this:

 8.2062

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:

\$8.21

Solution.  Here, the Base is missing.  Divide:

 8 4 . 6 ÷ 9 . 7 %

On the screen, see

 872.165

Again, this is money, so we must approximate it to two decimal places:

\$872.16

Example 6.   \$48.60 is what percent of \$96.40?

Solution.  The Percent is missing.  Divide:

Percent = Amount ÷ Base.

 4 8 . 6 ÷ 9 6 . 4 %

Again, it is not necessary to press the 0's on the end of decimals.

On the screen, see this decimal:

 50.4149

Let us round this off to one decimal place.  Since the digit in the second place is 1 (less than 5), we have

50.4%

 Summary Amount = Base × Percent Base = Amount ÷ Percent Percent = Amount ÷ Base

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

or

Continue on to the next Lesson.

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