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Adding and Subtracting with Negatives

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Adding and Subtracting with Negatives

Study Guide

Key Definition

The opposite of a number is also called its additive inverse. The additive inverse is the number you have to add to it so that the sum is zero. So the additive inverse of 5 is -5. This is sometimes called the property of opposites.

Important Notes

If you add any number to its opposite, or additive inverse, the answer is always zero.
When you add a positive number, you move to the right on the number line.
When you add a negative number, you move to the left on the number line.
When you subtract a positive number, you move to the left on the number line.
When you subtract a negative number, you move to the right on the number line.

Mathematical Notation

$-x$ means the opposite of $x$

$x + (-y)$ means subtract $y$ from $x$

$x - (-y)$ means add $y$ to $x$

Remember to use proper notation when solving problems

Why It Works

Working with negative numbers relies on the property of opposites and the number-line interpretation. Adding a negative is the same as subtracting a positive (move left), adding a positive moves right, subtracting a negative moves right, and subtracting a positive moves left. These ideas extend to any combination of positive and negative numbers.

Remember

Adding a positive and a negative number is like subtracting one value from the other.

Quick Reference

Property of Opposites:$x + (-x) = 0$

Understanding Adding and Subtracting with Negatives

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Adding a negative number is the same as subtracting a positive number. For example, $5 + (-2) = 5 - 2 = 3$. Subtracting a negative number is the same as adding a positive number. For example, $7 - (-4) = 7 + 4 = 11$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the result of $5 + (-3)$?

Real-World Problem

Question Exercise

Intermediate

Shopping Scenario

You owe your friend $10, but then you borrow another $5. How much do you owe in total?

Advanced Challenge

Thinking Exercise

Advanced

Think About This

You have $10, but you owe your friend $15. How much money will you have after you pay your friend?

Recap

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Review key concepts and takeaways