— Working With One —

Much of mathematics consists of working with the number one. Any number, other than zero (0), divided by itself equals one. We often have to use this concept while doing various forms of multiplication. This is because when a number is multiplied by one, its value is unchanged. The goal is to use one, writen in such a manner, as to allow us to accomplish a desired objective.

Some examples are given below.
(Look for the "ones" displayed in red.)

OBJECTIVEEXAMPLE
Reducing fractions
12
18
 =  2•2•3
3•2•3
 = 2
3
Converting the "divisor" to "one" in the division of fractions.
2
3
÷5
7
 =  2
3
5
7
 =  2
3
5
7
× 7
5

7
5
 = 
2
3
×7
5

1
Obtaining the "Lowest Common Denominator" of fractions to be added.
1
6
 +   1 
10
 +   1 
15
      6 = 2×3
10 = 2×5 
15 = 5×3 
LCD = 2×3×5= 30
1•5
6•5
  +    1•3
10•3
  +    1•2
15•2
 
 5 
30
  + 2 
30
  + 3 
30
 

 
Definition: "Per-Cent" means "by the hundred" or "Divided by one hundred."

English sentence: One hundred percent is the same as one hundred divided by one hundred.
Mathematical translation:100% = 100
100
or 100% = 1

English sentence: One percent is the same as one divided by one hundred.
Mathematical translation:1% =   1  
100
or 1% = 0.01

English sentence: Seventy-five percent is the same as seventy-five divided by one hundred.
Mathematical translation:75% =   75
100
or 75% = 0.75