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: The number line gives numbers geometric meaning: position and distance.

Common stuck point: Placing fractions and negatives correctly: -\frac{3}{4} is between -1 and 0, closer to -1.

Sense of Study hint: Draw tick marks for the integers first, then subdivide the spaces to place fractions. Mark zero clearly to anchor negative and positive sides.

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}.

Solution

  1. 1
    Convert to decimals for placement: -3 = -3, -\dfrac{1}{2} = -0.5, 0 = 0, 1.75 = 1.75, \dfrac{7}{3} \approx 2.33.
  2. 2
    Order from left to right: -3,\; -0.5,\; 0,\; 1.75,\; 2.33.
  3. 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.

Answer

Distance = \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 of -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.

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?
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Background Knowledge

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

countingintegers