Number Line Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Number Line.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A straight line where each point represents a number, with equal spacing giving a visual model of all real numbers. The number line extends infinitely in both directions, with negative numbers to the left of zero and positive numbers to the right, providing a geometric representation of order and distance.

Numbers live in order on a line—smaller to the left, larger to the right.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A number line places every number as a point in order, with equal gaps showing distance and direction.

Common stuck point: The procedure for number line is the easy part; the trap is spacing integers unevenly. Asking "Am I placing or comparing numbers as ordered, equally spaced points on a single line?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I placing or comparing numbers as ordered, equally spaced points on a single line?

Worked Examples

Example 1

easy

Plot and label the following on a number line:

-3

-\dfrac{1}{2}

0

1.75

\dfrac{7}{3}

. Then find the distance between

-3

and

\dfrac{7}{3}

Answer

Distance

= \dfrac{16}{3} \approx 5.33

First step

Convert to decimals for placement:

-3 = -3

-\dfrac{1}{2} = -0.5

0 = 0

1.75 = 1.75

\dfrac{7}{3} \approx 2.33

Full solution

2
Order from left to right: $-3,\; -0.5,\; 0,\; 1.75,\; 2.33$ .
3
Distance from $-3$ to $\dfrac{7}{3}$ : $\left|\dfrac{7}{3} - (-3)\right| = \left|\dfrac{7}{3} + 3\right| = \left|\dfrac{16}{3}\right| = \dfrac{16}{3} \approx 5.33$ .

The number line provides a geometric model for all real numbers. Distance between two points is the absolute value of their difference, so direction does not matter — only the magnitude of the gap. Converting to decimals makes ordering visual and intuitive.

Example 2

medium

Find all integers within distance

2.5

-1

on the number line.

Example 3

medium

On a number line, point A is at

-3

and point B is at

5

. Find the midpoint and the distance between them.

Example 4

medium

On a number line, point

A

is at

-2

and point

B

is at

6

. Point

C

is one-quarter of the way from

A

B

. Find

C

Example 5

medium

Find all integers within distance

4

-1

Example 6

hard

Solve

|x - 4| = 6

on the number line.

Example 7

hard

Sketch the set of

x

satisfying

|x| < 3

and describe it on the number line.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

On a number line, point

A

is at

-4

and point

B

is at

6

. Find the midpoint of

AB

and the distance

AB

Example 2

medium

A frog starts at

0

on a number line. It jumps

+5

, then

-3

, then

+7

, then

-9

. Where does it land, and what is the total distance travelled?

Example 3

easy

On a number line, which is farther to the right:

-2

3

Example 4

easy

How far apart are

2

and

7

on the number line?

Example 5

easy

Which point is to the left of

0

-1

4

Example 6

easy

What number is exactly halfway between

0

and

10

on the number line?

Example 7

easy

Order from least to greatest:

-3,\ 0,\ -1,\ 2

Example 8

easy

Where does

\frac{1}{4}

sit between

0

and

1

: closer to

0

or to

1

Example 9

easy

Is the spacing from

-3

-2

the same as from

2

3

Example 10

easy

What is the opposite of

5

on the number line?

Example 11

medium

A point is

4

units to the left of

1

on the number line. What number is it?

Example 12

medium

The distance between

x

and

3

5

, and

x < 3

. Find

x

Example 13

medium

Find the midpoint of

-6

and

4

on the number line.

Example 14

medium

On the line,

a

is left of

b

and both are negative. Which has the larger absolute value?

Example 15

medium

Between which two consecutive integers does

-2.7

lie?

Example 16

medium

A number is the same distance from

-1

as from

7

. What is it?

Example 17

medium

If you start at

-4

and move right by

9

units, where do you land?

Example 18

medium

List the integers strictly between

-2

and

3

on the number line.

Example 19

medium

Point

P

is at

2

. Point

Q

is its opposite. How far apart are

P

and

Q

Example 20

challenge

On a number line,

a<b

. Explain why the midpoint

m=\frac{a+b}{2}

always lies strictly between

a

and

b

Example 21

challenge

Points

A,B,C

sit on a line with

B

the midpoint of

A

and

C

. If

A=-5

and

B=1

, find

C

Example 22

challenge

A bug at

0

jumps right

\tfrac{1}{2}

, then right

\tfrac{1}{4}

, then

\tfrac{1}{8}

, halving each time forever. Does it ever pass

1

? Explain.

Example 23

easy

What is the distance between

-5

and

3

on a number line?

Example 24

easy

What number is halfway between

4

and

12

Example 25

easy

A bug at

-2

moves

7

units to the right. Where does it land?

Example 26

easy

Which of

-1.5

-0.5

is farther from

0

Example 27

easy

How far is

-3

from

0

on the number line?

Example 28

medium

On the number line, what is the midpoint of

-7

and

5

Example 29

medium

List all integers strictly between

-4

and

3

on the number line.

Example 30

medium

A snail starts at

0

, crawls

6

to the right, then

9

to the left. Where is it?

Example 31

medium

Order from least to greatest:

-\frac{1}{2}, 0.3, -1, \frac{1}{4}

Example 32

medium

Find

x

if the midpoint of

x

and

9

5

Example 33

medium

Plot

-\frac{5}{2}

on a number line. Between which two consecutive integers does it lie?

Example 34

medium

What is the opposite of

-7

Example 35

hard

A point

P

is twice as far from

0

as from

9

, and

P

is positive. Find

P

Example 36

hard

On a number line, three points

A, B, C

have

A = -3

C = 9

, and

B

is the midpoint of

A

and

C

. Find

B

, and then find the midpoint of

A

and

B

Example 37

hard

A frog at

0

takes jumps of

+3

and

-2

in any order. After

10

jumps total,

6

of them positive and

4

negative, where does the frog land?

Example 38

hard

Find

x

if the distance from

x

-2

5

and

x < 0

Example 39

hard

On a number line,

A = -4

and

B = 11

. Find the point that divides

\overline{AB}

in a

2:3

ratio from

A

Example 40

challenge

Three points on a number line have positions

a, b, c

with

a < b < c

, and

b

is the midpoint of

a

and

c

. If

a + b + c = 12

and

c - a = 6

, find

a, b, c

← Back to Number Line Formula Explained Practice Mode

Related Concepts

Counting Integers Coordinate Plane Absolute Value

Background Knowledge

These ideas may be useful before you work through the harder examples.

countingintegers