Find the Opposite Number: Determining the Additive Inverse of -8

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

The additive opposite of -8 is +8 (they add to zero). The reciprocal of -8 is -1/8 (they multiply to one). This problem asks for the reciprocal!

Q: Why is the reciprocal of -8 negative?

Because $ \frac{1}{-8} = -\frac{1}{8} $. The negative sign stays with the fraction. A negative number's reciprocal is always negative too.

Q: How do I remember the reciprocal formula?

Think "flip it" - if you have a number like -8, write it as $ \frac{-8}{1} $, then flip to get $ \frac{1}{-8} $ or $ -\frac{1}{8} $.

Reciprocal Operations with Negative Numbers

Convert $-8$ into its reciprocal form:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the reciprocal number

00:03 We will use the formula to find the reciprocal number

00:07 Any number multiplied by its reciprocal always equals 1

00:11 Note that the result is positive, therefore the number multiplication will be negative

00:16 Negative multiplied by negative always equals positive

00:21 And also negative divided by negative always equals positive

00:31 We swap between numerator and denominator to get the reciprocal number

00:37 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert $-8$ into its reciprocal form:

Step-by-step solution

To determine the opposite number of $-8$ according to the instructions, we need to find its reciprocal.

Step 1: Recall that the reciprocal of a number $a$ is defined as $\frac{1}{a}$ .
Step 2: Applying this definition, the reciprocal of $-8$ is $\frac{1}{-8}$ .
Step 3: Simplify $\frac{1}{-8}$ to $-\frac{1}{8}$ .

The result is $-\frac{1}{8}$ . Comparing this with the provided choices, we see that choice 3, $-\frac{1}{8}$ , is correct.

Therefore, the opposite number in the context of this problem is $\boxed{-\frac{1}{8}}$ , making the correct answer:

$-\frac{1}{8}$

Final Answer

$-\frac{1}{8}$

Key Points to Remember

Essential concepts to master this topic

Rule: The reciprocal of any number a is 1/a
Technique: For -8, write as 1/(-8) = -1/8
Check: Multiply -8 × (-1/8) = 1 to verify reciprocal ✓

Common Mistakes

Avoid these frequent errors

Confusing reciprocal with additive inverse
Don't find the opposite by just changing the sign from -8 to +8 = wrong concept! The reciprocal is multiplicative, not additive. Always use 1 divided by the original number.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$(+6)\cdot(+9)=$

FAQ

Everything you need to know about this question

What's the difference between opposite and reciprocal?

The additive opposite of -8 is +8 (they add to zero). The reciprocal of -8 is -1/8 (they multiply to one). This problem asks for the reciprocal!

Why is the reciprocal of -8 negative?

Because $\frac{1}{-8} = -\frac{1}{8}$ . The negative sign stays with the fraction. A negative number's reciprocal is always negative too.

How do I remember the reciprocal formula?

Think "flip it" - if you have a number like -8, write it as $\frac{-8}{1}$ , then flip to get $\frac{1}{-8}$ or $-\frac{1}{8}$ .

What if I get confused by the title mentioning 'opposite'?

Read the actual question carefully! The title says "opposite" but the question asks to "convert to reciprocal form." Always follow the specific instructions in the problem.

Can I check my reciprocal answer?

Yes! Multiply your answer by the original number. For reciprocals: $-8 \times \left(-\frac{1}{8}\right) = 1$ . If you get 1, you're correct!

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