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Equivalent Fractions

Note that a number of different divisions may have the same answer, for example:

          1/2=0.5, 2/4=0.5, 3/6=0.5, 4/8=0,5 ,    and so on.

Therefore, the fractions       one half = two fourths = three sixths = four eighths = 0.5

1 half = 2 fourths = 3 sixths = 4 eighths

Two fractions are equivalent if one is obtained from the other by multiplying or dividing the same number to both the numerator and the denominator. For example,

2/5 is equivalent to both (2*3)/(5*3)=6/15 and (2*4)/(5*4)=8/20 .

A fraction is irreducible if the numerator and denominator have no common factors (except 1). 2/5 is irredicible whereas 6 over 15 is reducible because 6 and 15 have a common factor of 3 and 6 over 15 is reducible because 8 and 20 have a common factor of 4.


In general, if (a*k)/(b*k)=c/d then c/d is equivalent to a/b.

Also, if (a/k)/(b/k)=c/d then c/d is equivalent to a/b.


The following shows an easy method of determining if two fractions are equivalent:


a/bis equivalent to c/d if and only if ad=bc.

cross multiply a times d and b times c



4/3=24/18 as 4*18=3*24=72

4/9 does not equal 92/197as 4*197 equals 788 which does not equal 9*92=828

More Examples (opens in seperate window)



Try the following exercises. Each time you click "New Exercise", a new exercise will appear. To answer each exercise, click on either the equality or inequality sign depending on which makes the statement true.





Try the following exercise. Click on the sign which makes the statement true. In this exercise, you are asked to determine if the reduced fraction is equivalent to the original fraction.




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