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WHAT PERCENT?

Lesson 29  Section 2


We have seen:

To change a number to a percent, multiply it by 100, and add the % sign.

(Lesson 3.)

Example 1.

.125  =  12.5%    To multiply by 100, move the point two places right.
 
2.6  =  260%    Move the point two places right.
 
8  =  800%    Multiply by 100:   Add on two 0's.

Example 2.   28 out of 63 people voted Yes.  What percent voted Yes?

Report the answer to one decimal digit.

Solution.  28 is what percent of 63?  Express 28 out of 63 as the fraction

   28
63		  , and multiply by 100.  
First, though, since 7 is a common divisor, reduce to  4
9		 .  Write
4
9		  × 100  =  400
  9 		  = 400 ÷ 9

To round off to one decimal digit, we must calculate two digits. (Lesson 11, Question 5.)

"9 goes into 40 four (4) times (36) with 4 left over." (Lesson 11.)

Again, "9 goes into 40 four (4) times with 4 left over."

Since the same remainder is repeated, this division will never be exact.  Therefore,

28 out of 63, which is equal to 4 out of 9, is approximately 44.4%.

Always:

A out of B =  A
B		  × 100%

To do this problem with a calculator, press

28 ÷ 63 %

See

 44.4444444

This is approximately 44.4%.

With a calculator, dividing approximates the fraction as a decimal. (Lesson 23.) The % key multiplies it by 100.
 3.   What is a general method for finding the Percent?
 
  Write the fraction that has the Base as the denominator and the Amount as the numerator, and express that fraction as a percent.
Amount
   Base		  = ? %

Certain fractions come up frequently, and the student should know their percent equivalents.  See Problem 18.

Example 3.   21 is what percent of 15?

Solution.   First, note that 21 is more than 15. Therefore it will be more than 100% of 15. (Lesson 16.)  On reducing and expressing the improper fraction as a mixed number:

21
15		   =   7
5		   =  1 2
5		 .
The percent will be 1 2
5		  × 100%. .

1 × 100% = 100%.

2
5		  × 100% ("Two fifths of 100%") = 40%.

(Lesson 26.)

21 is 140% of 15.


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