Negative Numbers Examples in Math

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

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

Concept Recap

Negative numbers are numbers less than zero, used to represent direction, deficit, or values below a reference point.

If zero is sea level, negative numbers are depths below the surface — temperature -5° is 5 degrees below freezing.

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 sign encodes direction: negative means below zero, opposite to positive. Adding a negative is the same as subtracting.

Common stuck point: Students treat negative sign as decoration rather than value direction.

Sense of Study hint: Use a number line and physically move left for negatives.

Worked Examples

Example 1

easy
The temperature was -8°\text{C} in the morning and rose by 15°\text{C} by noon. What was the noon temperature?

Solution

  1. 1
    Start at -8 and add 15: -8 + 15.
  2. 2
    Since 15 > 8, the result is positive: 15 - 8 = 7.
  3. 3
    The noon temperature was 7°\text{C}.

Answer

7°\text{C}
Adding a positive number to a negative number is equivalent to finding the difference and taking the sign of the number with the greater absolute value. Real-world contexts like temperature make negative numbers concrete.

Example 2

medium
Evaluate (-3)^2 - (-2)^3.

Practice Problems

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

Example 1

easy
Evaluate (-4) \times (-7) \times (-1).

Example 2

easy
A submarine is at -35 meters. It rises 12 meters and then sinks 7 meters. What is its final position?
← Back to Negative Numbers Practice Mode

Background Knowledge

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

integersnumber linesubtraction