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Equivalent Fractions

Two fractions are equivalent if they represent the same value.

For example, the figure below shows that 1 2 , 2 4 and 4 8 are all equivalent fractions -- in each figure, the shaded portion represents half of the whole circle.

In general, if you multiply the numerator and denominator of a fraction by the same (nonzero) number, you get a fraction equivalent to the one you started with. This is because when you multiply by a fraction like 2 2 or 7 7 , you're really just multiplying by 1 -- and multiplying by 1 always gives you the same number you started with. (Even if it looks different.)

For example:

2 5 = 2 7 5 7 = 14 35