Finding the Opposite of a Mixed Number

Oct 13, 2025 by recoveryshake.com 19 views

When dealing with numbers on a number line, it's essential to understand the concept of opposite numbers. The opposite of a number is the number that is the same distance from zero but in the opposite direction. In this case, we're given the number $-5 \frac{1}{2}$ and asked to find its opposite.

What are Opposite Numbers?

Opposite numbers are pairs of numbers that have the same absolute value but opposite signs. For example, the opposite of $5$ is $-5$ , and the opposite of $-3$ is $3$ . In the case of a mixed number like $-5 \frac{1}{2}$ , we need to find its opposite by changing the sign of the whole number part and the fraction part.

Finding the Opposite of a Mixed Number

To find the opposite of a mixed number, we need to follow these steps:

Change the sign of the whole number part.
Change the sign of the fraction part.

In the case of $-5 \frac{1}{2}$ , we have:

The whole number part is $-5$ , so its opposite is $5$ .
The fraction part is $\frac{1}{2}$ , so its opposite is $-\frac{1}{2}$ .

Therefore, the opposite of $-5 \frac{1}{2}$ is $5 - \frac{1}{2}$ .

Simplifying the Opposite Number

To simplify the opposite number, we can combine the whole number part and the fraction part:

$5 - \frac{1}{2} = \frac{10}{2} - \frac{1}{2} = \frac{9}{2}$

So, the opposite of $-5 \frac{1}{2}$ is $\frac{9}{2}$ .

Which Point Represents the Opposite Number?

Now that we have found the opposite number, we need to determine which point on the number line represents it. Looking at the options, we can see that:

Point P is at $-5$ .
Point Q is at $-3$ .
Point R is at $5$ .
Point S is at $5$ .

Since the opposite of $-5 \frac{1}{2}$ is $\frac{9}{2}$ , which is equal to $4 \frac{1}{2}$ , the correct answer is Point R.

Conclusion

In conclusion, the opposite of $-5 \frac{1}{2}$ is $5 - \frac{1}{2}$ , which simplifies to $\frac{9}{2}$ . Therefore, the point on the number line that represents the opposite number is Point R.

Key Takeaways

Opposite numbers are pairs of numbers that have the same absolute value but opposite signs.
To find the opposite of a mixed number, change the sign of the whole number part and the fraction part.
The opposite of $-5 \frac{1}{2}$ is $5 - \frac{1}{2}$ , which simplifies to $\frac{9}{2}$ .
The point on the number line that represents the opposite number is Point R.

Final Answer

Q: What is the opposite of a number?

A: The opposite of a number is the number that is the same distance from zero but in the opposite direction. For example, the opposite of $5$ is $-5$ , and the opposite of $-3$ is $3$ .

Q: How do I find the opposite of a mixed number?

A: To find the opposite of a mixed number, you need to follow these steps:

Change the sign of the whole number part.
Change the sign of the fraction part.

For example, the opposite of $-5 \frac{1}{2}$ is $5 - \frac{1}{2}$ .

Q: Can you explain the concept of opposite numbers in more detail?

A: Opposite numbers are pairs of numbers that have the same absolute value but opposite signs. For example, the opposite of $5$ is $-5$ , and the opposite of $-3$ is $3$ . This concept is essential in understanding various mathematical operations, such as addition and subtraction.

Q: How do I simplify the opposite of a mixed number?

A: To simplify the opposite of a mixed number, you can combine the whole number part and the fraction part. For example, the opposite of $-5 \frac{1}{2}$ is $5 - \frac{1}{2}$ , which simplifies to $\frac{9}{2}$ .

Q: What is the relationship between opposite numbers and the number line?

A: Opposite numbers are represented on the number line as points that are the same distance from zero but in the opposite direction. For example, the opposite of $-5$ is $5$ , which is represented by two points on the number line, one at $-5$ and the other at $5$ .

Q: Can you provide an example of finding the opposite of a number on the number line?

A: Let's consider the number $-5 \frac{1}{2}$ . To find its opposite, we need to change the sign of the whole number part and the fraction part. The opposite of $-5 \frac{1}{2}$ is $5 - \frac{1}{2}$ , which simplifies to $\frac{9}{2}$ . This point is represented on the number line as $4 \frac{1}{2}$ .

Q: How do I determine which point on the number line represents the opposite number?

A: To determine which point on the number line represents the opposite number, you need to look at the options and identify the point that corresponds to the opposite number. In the case of $-5 \frac{1}{2}$ , the opposite number is $\frac{9}{2}$ , which is equal to $4 \frac{1}{2}$ . Therefore, the correct answer is Point R.

Q: What is the significance of opposite numbers in mathematics?

A: Opposite numbers play a crucial role in various mathematical operations, such as addition and subtraction. Understanding the concept of opposite numbers is essential in solving problems and representing numbers on the number line.

Q: Can you provide a summary of the key takeaways from this article?

A: Here are the key takeaways from this article:

Opposite numbers are pairs of numbers that have the same absolute value but opposite signs.
To find the opposite of a mixed number, change the sign of the whole number part and the fraction part.
The opposite of $-5 \frac{1}{2}$ is $5 - \frac{1}{2}$ , which simplifies to $\frac{9}{2}$ .
The point on the number line that represents the opposite number is Point R.

Conclusion

In conclusion, opposite numbers are an essential concept in mathematics that plays a crucial role in various mathematical operations. Understanding the concept of opposite numbers is essential in solving problems and representing numbers on the number line. By following the steps outlined in this article, you can find the opposite of a mixed number and determine which point on the number line represents it.