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Equivalent Fractions

Equivalent Fractions have the same value, even though they may look different.

These fractions are really the same:
1  =  2  =  4
2 4 8

Why are they the same? Because when you multiply or divide both the top and bottom by the same number, the fraction keeps it's value. The rule to remember is:

What you do to the top of the fraction
you must also do to the bottom of the fraction !

So, here is why those fractions are really the same:

  × 2   × 2  
 
1  =  2  =  4
2 4 8
 
  × 2   × 2  
And visually it looks like this:

1/2   2/4   4/8
= =

Here are some more equivalent fractions, this time by dividing:

  ÷ 3   ÷ 6  
 
18  =  6  =  1
36 12 2
 
  ÷ 3   ÷ 6  

If we keep dividing until we can't go any further, then we have simplified the fraction (made it as simple as possible).

Important:

  • The top and bottom of the fraction must always be a whole number.
  • So, the number you pick to divide by must always divide evenly (ie no remainders) for both the top and bottom numbers.
  • You only multiply or divide, never add or subtract, to get an equivalent fraction.

A Chart of Fractions

We also have a chart of fractions with each row giving you examples of equivalent fractions.