Simplifying Fractions
Notice that the pictures of these fractions can be expressed as a number of different fractions.
2/6 are shaded yellow above and 1/3 is shaded yellow below. What do you notice about the size of the whole diagram above and the whole diagram below? They are the same size. What do you notice about the size of the yellow part in the diagram above and the yellow part in the diagram below? They are the same size. This means that 2/6 and 1/3 are equivalent fractions.
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What is an equivalent fraction of the 3/6 shaded pink above?
In the following circle fractions, shade 4/6 on the top left circle and 2/3 on the top right. Remember that the 3 says we have three equal parts in the whole.
In the following circle fractions, shade 3/6 on the left circle and 1/2 on the right. Remember that the 2 says we have two equal parts in the whole.
When we reduce the fraction, we basically remove, or
cancel, any common factors from the numerator and from the denominator. For
example: 
Notice that we removed two 2s from the numerator and two 2s from the denominator. Why is this possible?
What
does 
equal?
Why, one, of course! Remember that when we multiply by one, the answer never changes. The two sets of circle fractions are called equivalent fractions because they actually represent the same fractional area or parts. Also if you look at the top two fractions you’ll notice that both the numerator and denominator have common factors and they cancel.
