S k i l l
 i n
A R I T H M E T I C

Table of Contents | Home | Introduction

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 11.)

Example 1.

.48  =  48%    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%.

Division expresses the fraction as a decimal. (Lesson 23.) The % key multiplies it by 100.
 3.   What is a general method for finding the Percent?
 
15 is what percent of 20?
 
  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.   15 is what percent of 20?

Solution.  Write the fraction

Amount
   Base		  =  15
20
This reduces to  3
4		 .  But we know that three fourths of 100% --
3
4		  × 100%

-- is 75%.  15 is 75% of 20.


Equivalently, to ask

15 is what percent of 20?

is the same as asking

15 has what ratio to 20?

They have a common divisor 5.  "5 goes into 15 three times.   5 goes into 20 four times."  15 is three fourths of 20.  (Lesson 16, Question 7.)This means that 15 is 75% of 20.

Really, this should be a mental calculation.

Example 4.   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, and 9 goes into 18 two times, and into 27 three times.

18 is two thirds -- or 66 2
3		 % -- of 27.  (Lesson 15.)

Example 5.   20 is what percent of 8?

  Solution.    Amount
   Base		  =  20
 8		  = 2 4
8		  = 2½ = 250%.

20 is 250% of 8.  (2½ times 100% is 250%.)

Example 6.   .8 is what percent of 4?

  Solution.   Write the fraction  .8
 4		 , and clear of decimals.  Multiply both

terms by 10:

.8
 4		  =   8 
40
 8 
40		  =  1
5		 .  And  1
5		  = 20%.

.8 is 20% of 4.

Example 7.  Calculator problem.   7 is what percent of 11?

  Solution.  With a calculator,   Amount
   Base		   becomes  Amount ÷ Base.   Press
7 ÷ 11 %

(Lesson 13)  See

63.63636364

On rounding off to one decimal place, this is approximately

63.6%

Summary
 
A percent is a kind of fraction (ratio) whose denominator is understood to be 100.
 12 
100		 = 12%
There are two ways to express a number as a percent:
1.   The Method of Proportions.  Express the number as a
  fraction with denominator 100.
11 is what percent of 50?
11
50		  =    ?  
100		  =   22 
100		  = 22%
2.   The General Method.  Multiply the number -- the fraction
  -- times 100%.
11/50 × 100% = 22%

Please "turn" the page and do some Problems.

or


Introduction | Home | Table of Contents

Please make a donation to keep TheMathPage online.
Even $1 will help.

Copyright © 2001-2007 Lawrence Spector

Questions or comments?

E-mail:  themathpage@nyc.rr.com