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

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 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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