Find the Opposite Number: Converting -18 to Its Inverse

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

Great question! The opposite (additive inverse) of -18 is +18 because they add to zero. The reciprocal (multiplicative inverse) of -18 is $ -\frac{1}{18} $ because they multiply to 1!

Q: How do I remember what a reciprocal is?

Think "flip it!" For any number $ a $, its reciprocal is $ \frac{1}{a} $. For fractions like $ \frac{3}{4} $, flip to get $ \frac{4}{3} $!

Q: What happens when I multiply a number by its reciprocal?

You always get 1! That's the definition of reciprocal. For example: $ -18 \times (-\frac{1}{18}) = \frac{18}{18} = 1 $

Q: Can zero have a reciprocal?

No! Zero cannot have a reciprocal because $ \frac{1}{0} $ is undefined. You cannot divide by zero in mathematics!

Reciprocals with Negative Numbers

Convert $-18$ into its reciprocal form:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the inverse of a number together.

00:07 We'll use a formula for finding the inverse.

00:11 Remember, a number times its inverse gives us one.

00:15 If the result is positive, the number must be negative.

00:20 Multiplying two negatives always gives a positive result.

00:25 And dividing a negative by a negative is also positive.

00:29 Switch the numerator and denominator to find the inverse number.

00:40 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert $-18$ into its reciprocal form:

Step-by-step solution

To solve this problem, we need to find the opposite number of $-18$ .

Typically, the opposite of a number refers to its additive inverse, which would be $18$ . However, based on the problem context and subject information (determine the reciprocal), we interpret the task as finding the opposite reciprocal.

Step 1: Identify the given number, which is $-18$ .
Step 2: Calculate the reciprocal of $18$ , the positive component. The reciprocal of $18$ is $\frac{1}{18}$ .
Step 3: Since the original number is negative, the reciprocal also changes sign, becoming: $-\frac{1}{18}$ .

Hence, the opposite number of $-18$ considering the reciprocal context is $-\frac{1}{18}$ .

Therefore, the final answer is $-\frac{1}{18}$ .

Final Answer

$-\frac{1}{18}$

Key Points to Remember

Essential concepts to master this topic

Definition: The reciprocal of any number is 1 divided by that number
Technique: For -18, flip to get $\frac{1}{-18} = -\frac{1}{18}$
Check: Multiply original by reciprocal: $-18 \times (-\frac{1}{18}) = 1$ ✓

Common Mistakes

Avoid these frequent errors

Confusing reciprocal with additive inverse
Don't find the opposite by just changing the sign from -18 to +18 = wrong concept! The reciprocal means "flip the fraction" not "change the sign." Always remember: reciprocal of a number times the original equals 1.

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?

Great question! The opposite (additive inverse) of -18 is +18 because they add to zero. The reciprocal (multiplicative inverse) of -18 is $-\frac{1}{18}$ because they multiply to 1!

Why does the reciprocal of -18 stay negative?

The sign stays the same! When you flip -18 to get its reciprocal, you get $\frac{1}{-18}$ , which equals $-\frac{1}{18}$ . The negative sign travels with the number.

How do I remember what a reciprocal is?

Think "flip it!" For any number $a$ , its reciprocal is $\frac{1}{a}$ . For fractions like $\frac{3}{4}$ , flip to get $\frac{4}{3}$ !

What happens when I multiply a number by its reciprocal?

You always get 1! That's the definition of reciprocal. For example: $-18 \times (-\frac{1}{18}) = \frac{18}{18} = 1$

Can zero have a reciprocal?

No! Zero cannot have a reciprocal because $\frac{1}{0}$ is undefined. You cannot divide by zero in mathematics!

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