Equivalent Fractions - Cycle 2

A fraction is equivalent to another fraction when it represents the same part of a whole or set.

To fully understand what an equivalent fraction is, first you need to understand the role of the numerator and the denominator. To learn what a numerator and a denominator are, see The Representation of a Fraction.

It is important for the wholes to be identical - that is to say, they are the same size, as in the following image.

To verify that fractions are equivalent, I need to complete the following steps:

1. I represent the fraction of my choice.
2. I represent the second fraction using the same whole or set.
3. I compare the two fractions by observing the amounts used or shaded.

Alicia baked |12| cupcakes. |\dfrac{1}{3}| of her cupcakes have red frosting and |\dfrac{3}{12}| have blue frosting. All of the remaining cupcakes are white.

Did Alicia bake the same number of red cupcakes as blue cupcakes?

I represent the fraction of my choice. First, I choose to represent the fraction |\dfrac{3}{12}.| I know the total amount of cupcakes is |12| and the number of blue cupcakes is |\dfrac{3}{12}.|
I represent the second fraction using the same total. I know the total amount of cupcakes is |12| and that the quantity of red cupcakes is |\dfrac{1}{3}| of the total. Therefore, I need to divide the total amount of cupcakes into three equal groups and then pick one of the |3| groups.
I compare the two fractions by checking the quantities used or shaded. The first fraction indicates that Alicia made |3| blue cupcakes and the second fraction indicates she made |4| red cupcakes.

The amount of red cupcakes is not equivalent to the amount of blue cupcakes, because Alicia frosted |4| cupcakes red and only |3| cupcakes blue.

Therefore, |\dfrac{3}{12}| is not equivalent to |\dfrac{1}{3}.|