Find the Opposite Number of 7/2: Fraction Sign Change Problem

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

The reciprocal of $ \frac{7}{2} $ is $ \frac{2}{7} $ (flip the fraction). The opposite is $ -\frac{7}{2} $ (change the sign). They're completely different operations!

Q: Can I find the reciprocal of any fraction?

Yes, except for zero! Every non-zero fraction has a reciprocal. Just flip the numerator and denominator, keeping the same sign.

Q: What if I have a mixed number like 3½?

First convert to an improper fraction: $ 3\frac{1}{2} = \frac{7}{2} $. Then find the reciprocal: $ \frac{2}{7} $. Always work with improper fractions when finding reciprocals!

Reciprocal Operations with Proper Fractions

Convert $\frac{7}{2}$ into its reciprocal form:

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Understand the problem

Convert $\frac{7}{2}$ into its reciprocal form:

Step-by-step solution

To solve this problem, we recognize the task as finding the reciprocal of $\frac{7}{2}$ , given the provided solution to match.

Step 1: Identify the given rational number: $\frac{7}{2}$ .
Step 2: Determine the reciprocal: Flip the fraction to reverse the numerator and denominator.
Step 3: The reciprocal of $\frac{7}{2}$ is $\frac{2}{7}$ .

Therefore, the reciprocal of the given number $\frac{7}{2}$ is $\frac{2}{7}$ .

Final Answer

$\frac{2}{7}$

Key Points to Remember

Essential concepts to master this topic

Definition: Reciprocal means flip numerator and denominator positions
Method: For $\frac{7}{2}$ , flip to get $\frac{2}{7}$
Check: Multiply original by reciprocal: $\frac{7}{2} \times \frac{2}{7} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Confusing reciprocal with opposite number
Don't change the sign to get $-\frac{7}{2}$ = opposite, not reciprocal! The opposite changes sign, but reciprocal flips the fraction. Always flip numerator and denominator without changing the sign.

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?

The reciprocal of $\frac{7}{2}$ is $\frac{2}{7}$ (flip the fraction). The opposite is $-\frac{7}{2}$ (change the sign). They're completely different operations!

Why does the reciprocal of a fraction flip it?

By definition, a number times its reciprocal always equals 1. When you multiply $\frac{7}{2} \times \frac{2}{7}$ , the 7s and 2s cancel out to give $\frac{14}{14} = 1$ !

Can I find the reciprocal of any fraction?

Yes, except for zero! Every non-zero fraction has a reciprocal. Just flip the numerator and denominator, keeping the same sign.

What if I have a mixed number like 3½?

First convert to an improper fraction: $3\frac{1}{2} = \frac{7}{2}$ . Then find the reciprocal: $\frac{2}{7}$ . Always work with improper fractions when finding reciprocals!

How do I check if my reciprocal is correct?

Multiply the original number by your answer. If you get exactly 1, you're right! For example: $\frac{7}{2} \times \frac{2}{7} = \frac{14}{14} = 1$ ✓

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