LESSON: Equivalent Fractions

READ: Write Equivalent Fractions

Write Fractions Equivalent to a Given Fraction

What is a fraction?

A fraction is a part of a whole. When we work with fractions we think about the relationship between a part of something and the whole thing. Fractions show up all the time in real life. Sometimes, we don’t even realize that we are working with fractions because they are everywhere!

A fraction has two parts. It has a top number and a bottom number. The top number is called the numerator and tells us how many parts we have out of the whole. The bottom number is the denominator. It tells us how many parts the whole has been divided into.

Example

$\frac{4}{5}$ = means we have four out of five parts.

The four is our numerator it tells us how many parts we have.

The five is our denominator it tells us how many parts the whole has been divided into.

We can also show fractions in a visual way by using a picture.

Here our whole has been divided into ten parts. This is our denominator.

Five out of ten are shaded. This is our numerator.

$\frac{5}{10}$

We could also write the fraction that is not shaded. In this example it would be the same thing since five out of ten are shaded and five out of ten are not shaded.

Notice that $\frac{5}{10}$ are shaded and this is the same as $\frac{1}{2}$ of the whole being shaded. Because this whole has been divided into five parts, $\frac{5}{10}$ is the same as $\frac{1}{2}$ . These two fractions are equal or equivalent fractions.

What is an equivalent fraction? Equivalent Fractions are fractions that have the same value.

For example, $\frac{1}{2}$ is equivalent to the fractions below. The bars below visually represent why this is true.

If we add up each part then we have a fraction that is equivalent to one half

$\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8}$

The fractions below are equivalent to $\frac{1}{3}$ .

The bars below visually represent why this is true. The little numbers above each box show the number of sections that each whole has been divided into. Notice that this number is also the denominator.

We can write an equivalent set of fractions for one-third too.

$\frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{4}{12}$

Anytime that we want to create an equivalent fraction we multiply the numerator and denominator by the same number.

Example

Create a fraction equivalent to $\frac{3}{4}$ .

To do this, we need to multiply the numerator and denominator by the same number. Let’s choose 2. Two is always a good place to start.

$\frac{3 \times 2}{4 \times 2} &= \frac{6}{8}\\ \frac{6}{8} &= \frac{3}{4}$

We could create another equivalent fraction by choosing a different number. Let’s try four.

$\frac{3 \times 4}{4 \times 4} = \frac{12}{16}$

These fractions are also equivalent.