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Lesson 13

PERCENT
WITH 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.

(This follows from the relationship between multiplication and division, which we saw in Lesson 10.)


 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

Example 5.    $84.60 is 9.7% of how much? (Compare this with Example 4.)

Solution.  Here, the Base is missing.  Divide:

84 . 6 ÷ 9 . 7 %

On the screen, see

 872.16494 

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:

 50.41493 

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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