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

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a is negative number.

b is negative number.

What is the sum of a+b?

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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