Finding the Opposite Number of -4/3: Step-by-Step Solution

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

Great question! The reciprocal flips the fraction (numerator becomes denominator), while the opposite just changes the sign. For $ -\frac{4}{3} $: reciprocal is $ -\frac{3}{4} $, opposite is $ \frac{4}{3} $.

Q: How can I check if I found the right reciprocal?

Multiply them together! If you get 1 (or -1 for negative numbers), you're correct. $ -\frac{4}{3} \times -\frac{3}{4} = \frac{12}{12} = 1 $ ✓

Q: What if the question asks for the opposite instead?

Read carefully! Opposite means change the sign only. The opposite of $ -\frac{4}{3} $ would be $ \frac{4}{3} $ (positive), not the reciprocal.

Q: Can whole numbers have reciprocals too?

Absolutely! The reciprocal of any number n is $ \frac{1}{n} $. For example, the reciprocal of 5 is $ \frac{1}{5} $, and the reciprocal of -2 is $ -\frac{1}{2} $.

Reciprocal Operations with Negative Fractions

Convert $-\frac{4}{3}$ 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

00:03 Let's use the formula to find the reciprocal number

00:07 Any number multiplied by its reciprocal always equals 1

00:10 Note that the result is positive, so the number will be negative

00:13 Negative multiplied by negative always equals positive

00:19 And also negative divided by negative always equals positive

00:25 We'll swap between numerator and denominator to get the reciprocal number

00:32 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 $-\frac{4}{3}$ into its reciprocal form:

Step-by-step solution

To solve the problem of finding the opposite number of $-\frac{4}{3}$ , we'll follow these steps:

Step 1: Determine the reciprocal of the number.
Step 2: Change the sign of the resulting fraction to obtain the opposite number.

Let's work through each step in detail:

Step 1: The number given is $-\frac{4}{3}$ . To find its reciprocal, we invert the fraction, which switches the numerator and the denominator. Thus, the reciprocal of $-\frac{4}{3}$ is $-\frac{3}{4}$ .

Step 2: To find the opposite number, we must consider the sign change. The negative sign indicates the number is negative. Therefore, the opposite number, obtained by switching the sign, remains $-\frac{3}{4}$ , as a reciprocal operation already applied the sign change incorporation.

Therefore, the opposite number of $-\frac{4}{3}$ is $-\frac{3}{4}$ .

Final Answer

$-\frac{3}{4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Flip numerator and denominator to find reciprocal
Technique: Reciprocal of $-\frac{4}{3}$ becomes $-\frac{3}{4}$
Check: Multiply original by reciprocal: $-\frac{4}{3} \times -\frac{3}{4} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Changing the sign when finding reciprocal
Don't change the negative sign to positive when finding the reciprocal = wrong answer! The reciprocal of $-\frac{4}{3}$ is not $\frac{3}{4}$ . Always keep the same sign and only flip the numerator and denominator.

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 reciprocal and opposite?

Great question! The reciprocal flips the fraction (numerator becomes denominator), while the opposite just changes the sign. For $-\frac{4}{3}$ : reciprocal is $-\frac{3}{4}$ , opposite is $\frac{4}{3}$ .

Why does the negative sign stay the same?

The negative sign is part of the entire fraction, not just the numerator! When you flip $-\frac{4}{3}$ , you're flipping everything to get $-\frac{3}{4}$ .

How can I check if I found the right reciprocal?

Multiply them together! If you get 1 (or -1 for negative numbers), you're correct. $-\frac{4}{3} \times -\frac{3}{4} = \frac{12}{12} = 1$ ✓

What if the question asks for the opposite instead?

Read carefully! Opposite means change the sign only. The opposite of $-\frac{4}{3}$ would be $\frac{4}{3}$ (positive), not the reciprocal.

Can whole numbers have reciprocals too?

Absolutely! The reciprocal of any number n is $\frac{1}{n}$ . For example, the reciprocal of 5 is $\frac{1}{5}$ , and the reciprocal of -2 is $-\frac{1}{2}$ .

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