Practice Number Line in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick 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 lineβ€”smaller to the left, larger to the right.

Showing a random 20 of 50 problems.

Example 1

hard
Sketch the set of xx satisfying ∣x∣<3|x| < 3 and describe it on the number line.

Example 2

hard
A frog at 00 takes jumps of +3+3 and βˆ’2-2 in any order. After 1010 jumps total, 66 of them positive and 44 negative, where does the frog land?

Example 3

medium
Find the midpoint of βˆ’6-6 and 44 on the number line.

Example 4

medium
Plot βˆ’52-\frac{5}{2} on a number line. Between which two consecutive integers does it lie?

Example 5

easy
Where does 14\frac{1}{4} sit between 00 and 11: closer to 00 or to 11?

Example 6

easy
On a number line, point AA is at βˆ’4-4 and point BB is at 66. Find the midpoint of ABAB and the distance ABAB.

Example 7

medium
The distance between xx and 33 is 55, and x<3x < 3. Find xx.

Example 8

medium
On the number line, what is the midpoint of βˆ’7-7 and 55?

Example 9

easy
Order from least to greatest: βˆ’3,Β 0,Β βˆ’1,Β 2-3,\ 0,\ -1,\ 2.

Example 10

easy
Which point is to the left of 00: βˆ’1-1 or 44?

Example 11

medium
List the integers strictly between βˆ’2-2 and 33 on the number line.

Example 12

medium
Point PP is at 22. Point QQ is its opposite. How far apart are PP and QQ?

Example 13

easy
On a number line, which is farther to the right: βˆ’2-2 or 33?

Example 14

easy
Where does the fraction 12\frac{1}{2} sit on the number line between 00 and 11?

Example 15

medium
What is the opposite of βˆ’7-7?

Example 16

medium
Between which two consecutive integers does βˆ’2.7-2.7 lie?

Example 17

medium
List all integers strictly between βˆ’4-4 and 33 on the number line.

Example 18

hard
Solve ∣xβˆ’4∣=6|x - 4| = 6 on the number line.

Example 19

easy
What number is halfway between 44 and 1212?

Example 20

hard
Find xx if the distance from xx to βˆ’2-2 is 55 and x<0x < 0.