Master

Operations with Negatives

Master operations with negatives with interactive lessons and practice problems! Designed for students like you!

Learn

Get the basics

Practice

Apply your skills

Master

Achieve excellence

Operations with Negatives

Study Guide

Key Definition

Operations with negative numbers involve understanding that a negative times a negative is positive: $(-a)(-b) = ab$, while a positive times a negative is negative: $(a)(-b) = -ab$.

Important Notes

Adding a negative is like subtracting: $a + (-b) = a - b$
Subtracting a negative is like adding: $a - (-b) = a + b$
Multiplying two negatives gives a positive result: $(-a)(-b) = ab$
Division follows the same sign rules as multiplication.
Zero is neither positive nor negative.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

Negative numbers represent values less than zero. By understanding their properties, like $(-a)(-b) = ab$, we can simplify complex expressions.

Remember

When multiplying or dividing, if the signs are the same, the result is positive: $(-a)(-b) = ab$, $a/b$ when both are negative.

Quick Reference

Addition of Negatives:$-a + (-b) = -(a+b)$

Multiplication of Negatives:$(-a)(-b) = ab$

Understanding Operations with Negatives

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Simple explanation with $-a + a = 0$ and $(-a)(b) = -ab$

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $-3 + 5$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You owe your friend $\$10$. If you earn $\$25$, how much will you have after paying your friend back?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Find the result of $(-6) \times (-4)$ and explain why.

Challenge Quiz

Single Choice Quiz

Advanced

What is $\frac{-56}{-7}$?

Recap

Watch & Learn

Review key concepts and takeaways