Calculate the Inverse Number: Finding the Reciprocal of 5

Q: What's the difference between inverse and reciprocal?

Additive inverse (opposite) adds to zero: $ 5 + (-5) = 0 $. Multiplicative inverse (reciprocal) multiplies to one: $ 5 \times \frac{1}{5} = 1 $. Make sure you know which one the question is asking for!

Q: Why is the inverse of 5 equal to -5?

The additive inverse is the number that cancels out the original when added together. Since $ 5 + (-5) = 0 $, we know $ -5 $ is the correct inverse!

Q: What if the number is already negative?

Just flip the sign! The inverse of $ -3 $ is $ +3 $ (or just $ 3 $). Positive becomes negative, negative becomes positive.

Q: Does zero have an additive inverse?

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

Q: How do I remember which inverse to find?

Look for key words: "opposite" or "additive inverse" means change the sign. "Reciprocal" or "multiplicative inverse" means flip the fraction. When in doubt, additive inverse is more common in basic algebra.

Additive Inverses with Positive Integers

What is the inverse number of $5$

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Understand the problem

What is the inverse number of $5$

Step-by-step solution

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

Step 1: Identify the given number.
Step 2: Find its opposite by changing the sign.

Now, let's work through each step:
Step 1: The problem gives us the number $5$ .
Step 2: The opposite of a positive number is the same number with a negative sign.
Thus, the opposite of $5$ is $-5$ .

Therefore, the opposite number of $5$ is $-5$ .

Final Answer

$-5$

Key Points to Remember

Essential concepts to master this topic

Definition: Additive inverse means opposite number that adds to zero
Method: Change the sign: positive 5 becomes negative $-5$
Verify: Check that $5 + (-5) = 0$ ✓

Common Mistakes

Avoid these frequent errors

Confusing additive inverse with multiplicative inverse
Don't find $\frac{1}{5}$ when asked for inverse of 5 = wrong concept! This gives the reciprocal, not the opposite. Always remember additive inverse means the 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's the difference between inverse and reciprocal?

Additive inverse (opposite) adds to zero: $5 + (-5) = 0$ . Multiplicative inverse (reciprocal) multiplies to one: $5 \times \frac{1}{5} = 1$ . Make sure you know which one the question is asking for!

Why is the inverse of 5 equal to -5?

The additive inverse is the number that cancels out the original when added together. Since $5 + (-5) = 0$ , we know $-5$ is the correct inverse!

What if the number is already negative?

Just flip the sign! The inverse of $-3$ is $+3$ (or just $3$ ). Positive becomes negative, negative becomes positive.

Does zero have an additive inverse?

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

How do I remember which inverse to find?

Look for key words: "opposite" or "additive inverse" means change the sign. "Reciprocal" or "multiplicative inverse" means flip the fraction. When in doubt, additive inverse is more common in basic algebra.

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