Equivalent Fractions

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

These fractions are really the same:

12  =  24  =  48

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:

"Change the bottom using multiply or divide,
And the same to the top must be applied"

Here is why those fractions are really the same:

 × 2 × 2 
right over arrow   right over arrow
1 = 2 = 4
248
right under arrow   right under arrow
 × 2 × 2 
And visually it looks like this:

1/2 2/4 4/8
pie 1/2=pie 2/4=pie 4/8

 

See Fractions on the Number Line ...
fraction number line
... it shows many equivalent fractions.

Also see the Chart of Fractions with many examples of equivalent fractions.

Dividing

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

 ÷ 3 ÷ 6 
right over arrow   right over arrow
18 = 6 = 1
36122
right under arrow   right under arrow
 ÷ 3 ÷ 6 

Choose the number you divide by carefully, so that the results (both top and bottom) stay whole numbers.

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

 

Summary: