Find the Opposite Number of 4/5: Basic Fraction Properties

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

Great question! The additive opposite changes the sign (like $ -\frac{4}{5} $), but the reciprocal flips the fraction (like $ \frac{5}{4} $). This problem asks for reciprocal!

Q: Why do we flip the numerator and denominator?

The reciprocal is the multiplicative inverse - when you multiply a number by its reciprocal, you always get 1. That's why $ \frac{4}{5} \times \frac{5}{4} = \frac{20}{20} = 1 $!

Q: Can I just convert to decimal and flip it?

No! Converting $ \frac{4}{5} = 0.8 $ then flipping gives 8.0, which is wrong. Always work with fractions directly - flip numerator and denominator.

Q: How do I remember which is numerator and denominator?

Numerator is on top (like "up" has letters), denominator is on bottom (like "down" has letters). When finding reciprocal, top becomes bottom and bottom becomes top!

Reciprocal Operations with Fraction Properties

Convert $\frac{4}{5}$ 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 We'll use the formula to find a reciprocal number

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

00:09 We'll substitute the appropriate number according to the given data

00:17 We'll swap the numerator and denominator to get the reciprocal number

00:22 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 $\frac{4}{5}$ into its reciprocal form:

Step-by-step solution

To find the opposite of $\frac{4}{5}$ , we consider it from all reasonable interpretations:

Step 1: Given fraction is $\frac{4}{5}$ .
Step 2: Determine the additive opposite, changing the sign: $-\frac{4}{5}$ . This is traditional opposite term but unexpected in context described here.
Step 3: As the problem indicates opposite equals reciprocal, compute the reciprocal: The reciprocal of $\frac{4}{5}$ is $\frac{5}{4}$ . Understand direction subject suggestion.

Thus, by actor identity distinction or direction contrary to traditional rule sets, the reciprocal configuration yielded $\frac{5}{4}$ as central choice aligned fully in specified preferences.

Final Answer

$\frac{5}{4}$

Key Points to Remember

Essential concepts to master this topic

Definition: Reciprocal means flipping numerator and denominator positions
Technique: For $\frac{4}{5}$ , flip to get $\frac{5}{4}$
Check: Multiply original by reciprocal: $\frac{4}{5} \times \frac{5}{4} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Confusing reciprocal with additive opposite
Don't change the sign to get $-\frac{4}{5}$ = wrong concept! This is the additive opposite, not reciprocal. The reciprocal means multiplicative inverse. Always flip the numerator and denominator to find the reciprocal.

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?

Great question! The additive opposite changes the sign (like $-\frac{4}{5}$ ), but the reciprocal flips the fraction (like $\frac{5}{4}$ ). This problem asks for reciprocal!

Why do we flip the numerator and denominator?

The reciprocal is the multiplicative inverse - when you multiply a number by its reciprocal, you always get 1. That's why $\frac{4}{5} \times \frac{5}{4} = \frac{20}{20} = 1$ !

Can I just convert to decimal and flip it?

No! Converting $\frac{4}{5} = 0.8$ then flipping gives 8.0, which is wrong. Always work with fractions directly - flip numerator and denominator.

What if the fraction has a negative sign?

The negative sign stays with the fraction! For example, the reciprocal of $-\frac{3}{7}$ is $-\frac{7}{3}$ . Just flip the numbers, keep the sign.

How do I remember which is numerator and denominator?

Numerator is on top (like "up" has letters), denominator is on bottom (like "down" has letters). When finding reciprocal, top becomes bottom and bottom becomes top!

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