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EQUIVALENT FRACTIONS

Lesson 21  Section 2


 4.   How can we reduce a fraction in which the numerator or denominator is a decimal?
1.5
2
  Make both terms into whole numbers by multiplying them by the same power of 10.

This is called clearing of decimals.


  Example 1.   Clear of decimals and reduce:   1.5
 2

Solution.  To reduce a fraction, both the numerator and denominator must be whole numbers.  To make 1.5 into the whole number 15, multiply it by 10.  (Lesson 3, Question 2.)  Multiply 2 by 10 also:

1.5
 2		  =  15
20		  =  3
4		 .

15 and 20 have a common divisor 5.


  Now, after reducing  1.5
 2		 , we see that, proportionally,

1.5 is to 2  as  3 is to 4.

Therefore, if we ask, "What ratio has 1.5 to 2?", we can answer

1.5 is three fourths of 2.


  Example 2.   Clear of decimals and reduce:    .2 
.004

Solution.  To decide by which power of 10 to multiply, look at the number with the most number of decimal places; in this case, .004.  Therefore we will multiply both numbers by 1000:

  .2 
.004		 = 200
  4 		 = 50
 1		 = 50.

4 goes into 200 fifty times.

As for the ratio of .2 to .004, it is the same as 200 to 4, or 50 to 1.

.2 is fifty times .004.

We discover this important fact:

Decimals have the same ratio to one another as natural numbers.

Example 3.   What ratio has .07 to 1.4?

Answer.  Clear of decimals.  Multiply both numbers by 100:

.07
1.4		   =     7 
140		   =    1 
20		 .

.07 is to 1.4 in the same ratio as 1 is to 20.

.07 is the twentieth part of 1.4.


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