Equivalent Fractions | Elementary

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.

In this picture you can see that $2$ parts out of $3$ is equivalent to $4$ parts out of $6$ or $8$ parts out of $12.$ Thus, the amount shaded or used represents the same portion of the whole in each example.

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 $\dfrac{1}{3}.$

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.

In this picture you can see that $2$ parts out of $3$ is equivalent to $4$ parts out of $6$ or $8$ parts out of $12$. Thus, the amount shaded represents the same portion of the whole in each example.

To find an equivalent fraction using multiplication, I need to complete the following steps:

1. I determine by what number to multiply the fraction.

2. I multiply the numerator by that number.

3. I multiply the denominator by the same number.

Find a fraction equivalent to $\dfrac{4}{6}$ using multiplication.

I determine by what number I want to multiply the fraction. Here, I choose to multiply the fraction by $3.$
I multiply the numerator by that number.
I multiply the denominator by the same number.

$\dfrac{12}{18}$ is an equivalent fraction to $\dfrac{4}{6}.$

To find an equivalent fraction using division, I need to complete the following steps:

1. I determine the number I want to divide the fraction by.

2. I divide the numerator by that number.

3. I divide the denominator by the same number.

Find a fraction equivalent to $\dfrac{4}{6}$ by using division.

I determine the number I want to divide the fraction by. I need to make sure that the numerator and the denominator are both divisible by the number I choose. I know that both $4$ and $6$ are divisible by $2.$
I divide the numerator by that number.
I divide the denominator by the same number.

$\dfrac{2}{3}$ is an equivalent fraction to $\dfrac{4}{6}.$