Find the Multiplicative Inverse: Converting 12 to Its Reciprocal Form

Q: What exactly is a multiplicative inverse?

A multiplicative inverse (or reciprocal) is a number that when multiplied by the original number gives you 1. For 12, that's $ \frac{1}{12} $ because $ 12 \times \frac{1}{12} = 1 $.

Q: Why isn't the answer 1.2 or 0.12?

Those are decimal approximations, not exact reciprocals! The reciprocal of 12 is exactly $ \frac{1}{12} $, which equals about 0.0833... as a decimal, not 1.2 or 0.12.

Q: Does every number have a multiplicative inverse?

Almost every number! The only exception is zero - it has no reciprocal because you can't divide by zero. All other numbers have reciprocals.

Q: How do I check if my reciprocal is correct?

Simply multiply your answer by the original number. If you get 1, you're right! For this problem: $ \frac{1}{12} \times 12 = 1 $ ✓

Multiplicative Inverse with Whole Numbers

Convert 12 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 reciprocal of twelve.

00:07 We use a formula to find a reciprocal number.

00:10 Remember, any number times its reciprocal equals one.

00:15 Substitute twelve into the formula where the unknown is.

00:21 And that's how we solve the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert 12 into its reciprocal form:

Step-by-step solution

To solve the problem of finding the inverse of 12, we follow these steps:

Step 1: Identify the number given, which is 12.
Step 2: Apply the reciprocal formula to find the inverse, which is $\frac{1}{\text{number}}$ .

Now, let's work through the steps:
Step 1: We are given the number 12, and we need to find its inverse.
Step 2: Using the formula for the reciprocal, we have $\frac{1}{12}$ .
The reciprocal of a positive number is positive, so the inverse is $\frac{1}{12}$ .

Considering the answer choices provided, the correct choice is 3: $\frac{1}{12}$ .

Therefore, the inverse of 12 is $\frac{1}{12}$ .

Final Answer

$\frac{1}{12}$

Key Points to Remember

Essential concepts to master this topic

Definition: The multiplicative inverse of a number equals one divided by it
Formula: For any number n, the reciprocal is $\frac{1}{n}$
Check: Multiply original number by its reciprocal: $12 \times \frac{1}{12} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Confusing reciprocal with negative or decimal form
Don't write -1/12 or 1.2 for the reciprocal of 12 = completely wrong concept! The reciprocal is about division, not subtraction or decimals. Always use the formula 1/n where n is your original number.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

What exactly is a multiplicative inverse?

A multiplicative inverse (or reciprocal) is a number that when multiplied by the original number gives you 1. For 12, that's $\frac{1}{12}$ because $12 \times \frac{1}{12} = 1$ .

Why isn't the answer 1.2 or 0.12?

Those are decimal approximations, not exact reciprocals! The reciprocal of 12 is exactly $\frac{1}{12}$ , which equals about 0.0833... as a decimal, not 1.2 or 0.12.

Can negative numbers have reciprocals?

Yes! The reciprocal of a negative number is also negative. For example, the reciprocal of -5 is $-\frac{1}{5}$ . But since 12 is positive, its reciprocal $\frac{1}{12}$ is also positive.

Does every number have a multiplicative inverse?

Almost every number! The only exception is zero - it has no reciprocal because you can't divide by zero. All other numbers have reciprocals.

How do I check if my reciprocal is correct?

Simply multiply your answer by the original number. If you get 1, you're right! For this problem: $\frac{1}{12} \times 12 = 1$ ✓

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