8.09 Equivalent fractions on a number line
Are you ready?
Remembering how to compare fractions will help you solve problems in this lesson. Let's give this problem a try.
Think about the fractions $\frac{1}{4}$14 and $\frac{1}{5}$15.
Plot the number $\frac{1}{4}$14 on the number line.
Plot the number $\frac{1}{5}$15 on the number line.
The two numbers can be shown on the same number line like this:
Which number is smaller?
$\frac{1}{4}$14
A$\frac{1}{5}$15
B
Learn
We can show that two fractions are equal if they are the same point on a number line. Let's look at an example.
Let's show the fraction $\frac{3}{6}$36 on a number line. It looks like this:
Now let's show the fraction $\frac{2}{4}$24 on a number line. It looks like this:
As you can see, the number lines are split into different sized parts, but the two fractions $\frac{3}{6}$36 and $\frac{2}{4}$24 are the same length. This means that the two fractions are equal.
Apply
The fractions $\frac{1}{2}$12 and $\frac{2}{3}$23 are shown on the number lines below.
Are the two fractions equal?
Yes
ANo
B
If two fractions are at the same point on a number line, then those two fractions are the same size.