Find the Opposite Number: Converting -9⅓ to Its Inverse

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

The opposite (additive inverse) changes the sign: opposite of $ -9\frac{1}{3} $ is $ 9\frac{1}{3} $. The reciprocal (multiplicative inverse) flips the fraction after converting to improper form.

Q: Why do I need to convert mixed numbers first?

You can't directly flip a mixed number! You must convert $ -9\frac{1}{3} $ to $ -\frac{28}{3} $ first, then flip to get $ -\frac{3}{28} $.

Q: How do I convert a negative mixed number?

Keep the negative sign throughout! For $ -9\frac{1}{3} $: multiply whole number by denominator (9 × 3 = 27), add numerator (27 + 1 = 28), keep negative sign: $ -\frac{28}{3} $.

Q: What does it mean when a number times its reciprocal equals 1?

This is the definition of reciprocals! Any non-zero number multiplied by its reciprocal always equals 1. It's how we verify our answer is correct.

Q: Can zero have a reciprocal?

No! Zero has no reciprocal because you cannot divide by zero. The reciprocal of $ a $ is $ \frac{1}{a} $, and $ \frac{1}{0} $ is undefined.

Reciprocal Operations with Mixed Numbers

Convert $-9\frac{1}{3}$ 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

00:04 Use the formula to find the reciprocal number

00:07 Break down the mixed fraction into a whole number and a fraction

00:17 Convert from the whole number to a complete fraction

00:33 And we'll get the fraction

00:49 Any number multiplied by its reciprocal always equals 1

01:00 Switch between numerator and denominator to get the reciprocal number

01:05 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 $-9\frac{1}{3}$ into its reciprocal form:

Step-by-step solution

To solve the problem of finding the opposite number of $-9\frac{1}{3}$ , we will treat the requirement as finding the reciprocal of this number:

Step 1: Convert the mixed number to an improper fraction.

The mixed number $-9\frac{1}{3}$ implies a sign still applies after conversion. We compute: $-9 = -\frac{27}{3}$ , and adding $-\frac{1}{3}$ results in the improper fraction $-\frac{28}{3}$ .

Step 2: Find the reciprocal of the improper fraction.

The reciprocal of $-\frac{28}{3}$ is $-\frac{3}{28}$ .

Based on the above steps, the reciprocal of $-9\frac{1}{3}$ is indeed $-\frac{3}{28}$ .

Thus, the opposite number of $-9\frac{1}{3}$ , interpreted as its reciprocal, is $-\frac{3}{28}$ .

Final Answer

$-\frac{3}{28}$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Transform mixed numbers to improper fractions first
Technique: For $-9\frac{1}{3}$ , compute $-\frac{27+1}{3} = -\frac{28}{3}$
Check: Multiply reciprocal by original: $-\frac{3}{28} \times -\frac{28}{3} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Finding the opposite (additive inverse) instead of reciprocal
Don't change $-9\frac{1}{3}$ to $9\frac{1}{3}$ = wrong concept! The opposite means additive inverse, but reciprocal means multiplicative inverse. Always flip the fraction after converting to improper form.

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 opposite and reciprocal?

The opposite (additive inverse) changes the sign: opposite of $-9\frac{1}{3}$ is $9\frac{1}{3}$ . The reciprocal (multiplicative inverse) flips the fraction after converting to improper form.

Why do I need to convert mixed numbers first?

You can't directly flip a mixed number! You must convert $-9\frac{1}{3}$ to $-\frac{28}{3}$ first, then flip to get $-\frac{3}{28}$ .

How do I convert a negative mixed number?

Keep the negative sign throughout! For $-9\frac{1}{3}$ : multiply whole number by denominator (9 × 3 = 27), add numerator (27 + 1 = 28), keep negative sign: $-\frac{28}{3}$ .

What does it mean when a number times its reciprocal equals 1?

This is the definition of reciprocals! Any non-zero number multiplied by its reciprocal always equals 1. It's how we verify our answer is correct.

Can zero have a reciprocal?

No! Zero has no reciprocal because you cannot divide by zero. The reciprocal of $a$ is $\frac{1}{a}$ , and $\frac{1}{0}$ is undefined.

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