Find the Additive Inverse: Determining the Opposite of 87

Q: What exactly is an additive inverse?

An additive inverse is the opposite number that, when added to the original number, gives you zero. For 87, its additive inverse is $ -87 $ because $ 87 + (-87) = 0 $.

Q: Is there a difference between 'opposite' and 'additive inverse'?

No difference at all! These terms mean exactly the same thing. Both refer to the number that adds with the original to make zero.

Q: What about negative numbers - do they have additive inverses too?

Absolutely! The additive inverse of $ -5 $ is $ +5 $ (or just 5). Every real number has an additive inverse.

Q: Why do we need additive inverses in math?

Additive inverses help us subtract and solve equations! When we subtract 87, we're really adding its additive inverse: $ 100 - 87 = 100 + (-87) $.

Q: Does zero have an additive inverse?

Yes! The additive inverse of zero is zero itself because $ 0 + 0 = 0 $. Zero is special - it's its own opposite.

Additive Inverse with Positive Integers

What is the additive inverse number of $87$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the additive inverse number of $87$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given number
Step 2: Apply the definition of an opposite number
Step 3: Conclude with the opposite number

Now, let's work through each step with detailed explanations:
Step 1: We are given the number $87$ . This is a positive integer.
Step 2: The definition of an opposite number states that the opposite of any number $x$ is $-x$ . Here, $x = 87$ .
Step 3: Using the definition, the opposite number of $87$ is calculated as $-87$ .

Therefore, the solution to the problem is $-87$ .

Final Answer

$-87$

Key Points to Remember

Essential concepts to master this topic

Definition: The additive inverse of any number is its opposite
Technique: Change the sign: positive 87 becomes $-87$
Verification: Add original and inverse: $87 + (-87) = 0$ ✓

Common Mistakes

Avoid these frequent errors

Confusing additive inverse with multiplicative inverse
Don't think the additive inverse of 87 is 1/87 = wrong concept! That's the multiplicative inverse (reciprocal), not the additive inverse. Always remember additive inverse means the opposite number that adds to zero.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

What exactly is an additive inverse?

An additive inverse is the opposite number that, when added to the original number, gives you zero. For 87, its additive inverse is $-87$ because $87 + (-87) = 0$ .

Is there a difference between 'opposite' and 'additive inverse'?

No difference at all! These terms mean exactly the same thing. Both refer to the number that adds with the original to make zero.

What about negative numbers - do they have additive inverses too?

Absolutely! The additive inverse of $-5$ is $+5$ (or just 5). Every real number has an additive inverse.

Why do we need additive inverses in math?

Additive inverses help us subtract and solve equations! When we subtract 87, we're really adding its additive inverse: $100 - 87 = 100 + (-87)$ .

Does zero have an additive inverse?

Yes! The additive inverse of zero is zero itself because $0 + 0 = 0$ . Zero is special - it's its own opposite.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Signed Numbers (Positive and Negative) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime