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 		 Exploring whole numbers ( Number Operations & Number Theory )
Term    : 1 
Module : 1 - Capturing Data 
Unit 1    : Numbers Made Easy (  Rational Numbers ) - 
                Properties & Special Operations                                               
                                  EQUIVALENT FRACTIONS  		 
Equivalent
Fraction
(Example)
 

Equivalent Fractions   - are equal fractions.
Two fractions are equivalent if they represent the same amount.
Although the numbers may look different, calculations will show that equivalent fractions are equal, or are the same fractions.
If a pizza is divided into 8 equal slices, and you get 4 of the 8 slices, then it is the same as receiving half.
This just means that the same pizza was divided into 2, and you got 1 of the 2 portions which is half.
 

 

  
Equivalent
Fraction
(Diagram)

 

 

  
Equivalent
Fraction
(Create)		 You can create an equivalent fraction, by multiplying the numerator and the denominator of a fraction by the same number, or dividing the numerator and the denominator of a fraction by the same factor.

To create or find equivalent fractions it is important to know the prime factors of both the numerator and the denominator.
You can use any of the two methods shown in the diagram below to find the prime factorization of a number.
 

  
Prime
Factorization		  
Simplifying
Fractions
 		 You can use prime factors of both the numerator and the denominator to determine equivalent fractions, as well as to simplify fractions.

In the example the fraction 4/12 is simplified forming a new equivalent fraction 1/3.

Steps To Simplify Fractions:
(1) Find the prime factors of both the numerator and the denominator.
(2) Cancel out all common factors.
 

  
Cancelling
common
Factors
 
 		  
Higher
Terms
 		 Whenever an equivalent fraction is needed with larger numbers in the numerator and the denominator, we build the fraction or express the fraction in higher terms.

Steps For Expressing A Fraction In Higher Terms:
(1) Multiply the numerator by any required number.
(2) Multiply the denominator by that same number.
 

Note: According to the Fundamental Properties Of Fractions, the resulting fraction has the same value and is therefore an equivalent fraction.


 

  
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