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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, Question 10.)

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.   7 out of 12 people voted Yes.  What percent voted Yes?

   Solution.   Express 7 out of 12 as the fraction   7 
12		  , and multiply by 100.

Write

 7 
12		  × 100  =  700
 12		  = 700 ÷ 12

"12 goes into 70 five (5) times (60) with 10 left over."  (Lesson 11.)

"12 goes into 100 eight (8) times (96) with 4 left over."

 The fraction   4 
12		  reduces to  1
3		 .  Therefore,
7 out of 12 = 58 1
3		 %.

Always:

A out of B =  A
B		  × 100%

To do this problem with a calculator, press

7 ÷ 12 %

See

 58.3333333 

This is approximately 58.3%.

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?
 
21 is what percent of 28?
 
  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 17 at the end of the Lesson.

Example 3.   21 is what percent of 28?

Solution.  Write the fraction

Amount
   Base		  =  21
28		 .
This reduces to  3
4		 .  But we know that three fourths of 100% --
3
4		  × 100%

-- is 75%.  21 is 75% of 28.

Equivalently, to ask

21 is what percent of 28?

is the same as asking

21 has what ratio to 28?

They have a common divisor 7.  Therefore,

21 is to 28  as  3 is to 4.

And 3 is three fourths of 4. (Lesson 16.)  Therefore, 21 is three fourths, or 75%, of 28.

Really, this should be a mental calculation.  In fact, if the student knows the percent in each of the following, then the student will understand any percent problem that does not require a calculator.  In each of the following, the two numbers are the smallest -- the lowest terms -- which have that ratio.  For, a percent is a ratio.

To see the answer, pass your mouse over the colored area.
To cover the answer again, click "Refresh" ("Reload").
Do the problem yourself first!

1 is 50% of 2.

See Lesson 27, Problem 1.

1 is 25% of 4.

3 is 75% of 4.

1 is 12½% of 8.

1 is  33 1
3		 % of 3.   (Lesson 15.)
 
2 is  66 2
3		 % of 3.

1 is 20% of 5.

2 is 40% of 5.

3 is 60% of 5.

4 is 80% of 5.

1 is 10% of 10.

2 is 200% of 1.

3 is 300% of 1.

5 is 250% of 2.

13 is 325% of 4.

Example 4.   14 is what percent of 35?

Answer.  14 and 35 have a common divisor 7.  Therefore,

14 is to 35  as  2 is to 5.

That is,

14 is the same percent of 35  that  2 is of 5 -- which is 40%.

Example 5.   What percent of 27 is 18?

Solution.  The Base is 27 -- it follows "of."  In standard form:

18 is what percent of 27?

Now, 9 is a common divisor.  Therefore,

18 is to 27  as  2 is to 3.

18 is 66 2
3		 % of 27.

Example 6.   20 is what percent of 8?

Answer.   Their common divisor is 4.  Therefore they have the same ratio that 5 has to 2, which is two and a half times:

20 is 250% of 8.

Example 7.   .8 is what percent of 4?

Answer.   Make both numbers whole numbers by multiplying by 10:

.8 is to 4  as  8 is to 40  as  1 is to 5.

.8 is 20% of 4.

Example 8.   7 is what percent of 11?

Answer.   This is a calculator problem  Press

7 ÷ 11 %

(Lesson 13.)  See

63.63636364

On rounding off to one decimal place, this is approximately

63.6%.


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