Find the Opposite Number: Determining the Negative of 49

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

Great question! The opposite (additive inverse) of 49 is -49 because 49 + (-49) = 0. The reciprocal (multiplicative inverse) of 49 is $ \frac{1}{49} $ because $ 49 \times \frac{1}{49} = 1 $.

Q: Why is the question asking for reciprocal but calling it 'opposite number'?

This can be confusing! Sometimes multiplicative inverse (reciprocal) is called the 'opposite' in multiplication contexts. The key clue is that the correct answer is $ \frac{1}{49} $, which confirms we need the reciprocal.

Q: How do I find the reciprocal of any number?

Simple! Just flip it into a fraction: reciprocal of a = $ \frac{1}{a} $. For 49, flip it to get $ \frac{1}{49} $. For $ \frac{3}{4} $, flip to get $ \frac{4}{3} $!

Q: Can negative numbers have reciprocals?

Yes! The reciprocal of -5 is $ \frac{1}{-5} = -\frac{1}{5} $. The reciprocal keeps the same sign as the original number.

Q: What happens when I multiply a number by its reciprocal?

You always get 1! This is the defining property of reciprocals: $ a \times \frac{1}{a} = 1 $ for any non-zero number a.

Reciprocal Operations with Positive Integers

Convert $49$ 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 swap between numerator and denominator to get the reciprocal number

00:14 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 $49$ into its reciprocal form:

Step-by-step solution

To solve this problem, we need to find the reciprocal of $49$ because the problem refers to the "opposite number," in this context, likely meaning its multiplicative inverse.

Here are the steps to find the solution:

Step 1: Start with the given number, which is $49$ .
Step 2: Apply the formula for the reciprocal. The reciprocal of a number $a$ is $\frac{1}{a}$ .
Step 3: Substitute $49$ for $a$ in the formula, resulting in the reciprocal being $\frac{1}{49}$ .

Thus, the reciprocal or "opposite number" of $49$ is $\frac{1}{49}$ .

To confirm with the answer choices, the correct choice is $\frac{1}{49}$ .

Therefore, the solution to the problem is $\frac{1}{49}$ .

Final Answer

$\frac{1}{49}$

Key Points to Remember

Essential concepts to master this topic

Definition: The reciprocal of a number is 1 divided by that number
Formula: For any number a, its reciprocal is $\frac{1}{a}$
Check: Multiply number by its reciprocal: $49 \times \frac{1}{49} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Confusing reciprocal with additive inverse (opposite)
Don't think 'opposite number' means -49 = negative version! This confuses additive inverse with multiplicative inverse. The reciprocal involves division, not subtraction. Always remember: reciprocal means $\frac{1}{\text{number}}$ , not negative of the number.

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 opposite (additive inverse) of 49 is -49 because 49 + (-49) = 0. The reciprocal (multiplicative inverse) of 49 is $\frac{1}{49}$ because $49 \times \frac{1}{49} = 1$ .

Why is the question asking for reciprocal but calling it 'opposite number'?

This can be confusing! Sometimes multiplicative inverse (reciprocal) is called the 'opposite' in multiplication contexts. The key clue is that the correct answer is $\frac{1}{49}$ , which confirms we need the reciprocal.

How do I find the reciprocal of any number?

Simple! Just flip it into a fraction: reciprocal of a = $\frac{1}{a}$ . For 49, flip it to get $\frac{1}{49}$ . For $\frac{3}{4}$ , flip to get $\frac{4}{3}$ !

Can negative numbers have reciprocals?

Yes! The reciprocal of -5 is $\frac{1}{-5} = -\frac{1}{5}$ . The reciprocal keeps the same sign as the original number.

What happens when I multiply a number by its reciprocal?

You always get 1! This is the defining property of reciprocals: $a \times \frac{1}{a} = 1$ for any non-zero number a.

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