Math Core

You already know where 1, 2 and 3 live on a number line. Fractions have spots too! They live in the spaces between the whole numbers.

The whole is the space from 0 to 1

On a number line, the whole is the distance from 0 to 1. To show fourths, cut that space into 4 equal lengths.

Each small length is $\dfrac{1}{4}$ of the whole. The first tick after 0 is at $\dfrac{1}{4}$ , because it is 1 fourth away from 0.

Fractions on a number line

To place $\dfrac{a}{b}$ on a number line:

Cut the space from 0 to 1 into $b$ equal lengths.
Start at 0 and count $a$ of those lengths.
Where you stop is $\dfrac{a}{b}$ .

Hopping to a fraction

To find $\dfrac{3}{4}$ , start at 0 and make 3 hops. Each hop is $\dfrac{1}{4}$ long.

One fourth, two fourths, three fourths. The dot is at $\dfrac{3}{4}$ .

Here is a number line cut into thirds. The dot is 2 hops from 0, so it is at $\dfrac{2}{3}$ .

Common mistake

Count the spaces, not the tick marks! A line from 0 to 1 with 4 equal spaces has 5 tick marks (including 0 and 1). The denominator is the number of spaces: 4.

Worked example: What fraction is the dot?

What fraction does the dot show?

Count the spaces between 0 and 1: there are 6, so each one is $\dfrac{1}{6}$ . The dot is 5 spaces from 0. It shows $\dfrac{5}{6}$ .

Worked example: Place a fraction

Where does $\dfrac{3}{8}$ go on a number line?

Cut the space from 0 to 1 into 8 equal lengths. Start at 0 and count 3 lengths.

Worked example: Distance from 0

On a number line cut into sixths, Ben stops at the 4th tick after 0. How far is he from 0? How far is he from 1?

He made 4 hops of $\dfrac{1}{6}$ , so he is $\dfrac{4}{6}$ from 0. There are 6 sixths from 0 to 1, and $6 - 4 = 2$ , so he is $\dfrac{2}{6}$ away from 1.

Tip

The last tick in every fraction line, at 1, can also be named with the same denominator: $\dfrac{4}{4}$ on a fourths line, $\dfrac{3}{3}$ on a thirds line. You will see more of this soon.

Practice

Practice 1

What fraction does the dot show?

Type your answer like 1/3.

Type a number.

Practice 2

A number line from 0 to 1 is cut into fourths. How many equal spaces are between 0 and 1?

Type a number.

Practice 3

What fraction does the dot show?

Type your answer like 1/3.

Type a number.

Practice 4

Kim says the dot below shows $\dfrac{1}{4}$ because there are 4 tick marks. What fraction does it really show?

Practice 5

What fraction does the dot show?

Type your answer like 1/3.

Type a number.

Practice 6

To get from 0 to $\dfrac{3}{6}$ on a number line, how many hops of $\dfrac{1}{6}$ do you make?

Type a number.

Practice 7

A frog sits at $\dfrac{2}{3}$ on a number line. How much farther must it hop to reach 1?

Type your answer like 1/2.

Type a number.