Calculate the Multiplicative Inverse: Finding 1/3

Q: What's the difference between multiplicative inverse and additive inverse?

Multiplicative inverse (reciprocal) gives 1 when multiplied with the original number. Additive inverse (opposite) gives 0 when added. For 3: reciprocal is $ \frac{1}{3} $, opposite is -3.

Q: Why is the reciprocal of 3 written as a fraction?

Because $ \frac{1}{3} $ is the exact answer! Writing it as 0.333... loses precision since the decimal repeats forever. Fractions give us the most accurate representation.

Q: Can I check my answer using multiplication?

Yes! The best way to verify is multiplying your answer by the original number. If you get 1, you're correct: $ 3 \times \frac{1}{3} = \frac{3}{3} = 1 $ ✓

Multiplicative Inverse with Reciprocal Calculation

What is the inverse of 3?

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Step-by-step video solution

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00:00 Find what is the reciprocal number of 3

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

00:06 Any number multiplied by its reciprocal always equals 1

00:09 We'll substitute 3 in the unknown according to the given

00:12 And this is the solution to the question

Step-by-step written solution

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Understand the problem

What is the inverse of 3?

Step-by-step solution

To solve this problem, we need to find the inverse of the number 3. In mathematics, the term "inverse" in this context refers to the multiplicative inverse. The multiplicative inverse or reciprocal of a number is defined as a number which, when multiplied by the original number, gives a product of 1.

Given the number 3, its reciprocal is calculated by dividing 1 by the number:

$\text{Reciprocal of 3} = \frac{1}{3}$

This means that the multiplicative inverse of 3 is $\frac{1}{3}$ .

Therefore, the solution to the problem is $\frac{1}{3}$ .

Final Answer

$\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Definition: Multiplicative inverse means dividing 1 by the original number
Formula: Reciprocal of 3 = $\frac{1}{3}$ using division
Check: Verify by multiplying: $3 \times \frac{1}{3} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Confusing multiplicative inverse with additive inverse
Don't think the inverse of 3 is -3 = wrong type of inverse! The additive inverse (opposite) gives you zero when added, but multiplicative inverse gives you 1 when multiplied. Always use $\frac{1}{n}$ for multiplicative inverse.

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's the difference between multiplicative inverse and additive inverse?

Multiplicative inverse (reciprocal) gives 1 when multiplied with the original number. Additive inverse (opposite) gives 0 when added. For 3: reciprocal is $\frac{1}{3}$ , opposite is -3.

Why is the reciprocal of 3 written as a fraction?

Because $\frac{1}{3}$ is the exact answer! Writing it as 0.333... loses precision since the decimal repeats forever. Fractions give us the most accurate representation.

How do I find the reciprocal of any number?

Simply put 1 over that number! For any number n, its reciprocal is $\frac{1}{n}$ . For example: reciprocal of 7 is $\frac{1}{7}$ , reciprocal of 0.5 is $\frac{1}{0.5} = 2$ .

Can I check my answer using multiplication?

Yes! The best way to verify is multiplying your answer by the original number. If you get 1, you're correct: $3 \times \frac{1}{3} = \frac{3}{3} = 1$ ✓

What happens with negative numbers?

The reciprocal of a negative number is also negative! For example, reciprocal of -3 is $\frac{1}{-3} = -\frac{1}{3}$ . The sign stays the same in reciprocals.

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