Which Expression Is $\frac{1}{2}$ As Large As $486-466$?Choose One Answer:A. $486-466 \times \frac{1}{2}$ B. $\frac{1}{2} \times (486-466$\] C. $(486+466) \times \frac{1}{2}$

Which Expression is $\frac{1}{2}$ as Large as $486-466$?

Understanding the Problem

When dealing with mathematical expressions, it's essential to understand the concept of equivalence and proportionality. In this problem, we're asked to find an expression that is $\frac{1}{2}$ as large as the result of $486-466$. To approach this, we need to understand what it means for an expression to be $\frac{1}{2}$ as large as another.

The Concept of Proportionality

Proportionality is a fundamental concept in mathematics that describes the relationship between two quantities. In this case, we're looking for an expression that is proportional to the result of $486-466$. This means that the expression should be a multiple of the result, where the multiple is $\frac{1}{2}$.

Analyzing the Options

Let's analyze each of the given options to determine which one represents an expression that is $\frac{1}{2}$ as large as $486-466$.

Option A: $486-466 \times \frac{1}{2}$

This option involves multiplying the result of $486-466$ by $\frac{1}{2}$. However, this would actually reduce the result by half, rather than increasing it by half. Therefore, this option is not correct.

Option B: $\frac{1}{2} \times (486-466)$

This option involves multiplying the result of $486-466$ by $\frac{1}{2}$. This would indeed reduce the result by half, rather than increasing it by half. Therefore, this option is not correct.

Option C: $(486+466) \times \frac{1}{2}$

This option involves multiplying the sum of $486$ and $466$ by $\frac{1}{2}$. However, this would actually reduce the sum by half, rather than increasing the result of $486-466$ by half. Therefore, this option is not correct.

The Correct Answer

After analyzing each of the options, we can see that none of them directly represent an expression that is $\frac{1}{2}$ as large as $486-466$. However, we can use the concept of proportionality to find the correct answer.

The Correct Expression

To find an expression that is $\frac{1}{2}$ as large as $486-466$, we can use the following logic:

• If $x$ is the result of $486-466$, then $\frac{1}{2}x$ is $\frac{1}{2}$ as large as $x$.
• Therefore, the expression we're looking for is $\frac{1}{2}(486-466)$.

Simplifying the Expression

To simplify the expression, we can evaluate the result of $486-466$ first:

$486-466 = 20$

Now, we can multiply the result by $\frac{1}{2}$:

$\frac{1}{2} \times 20 = 10$

Therefore, the expression that is $\frac{1}{2}$ as large as $486-466$ is $\boxed{10}$.

Conclusion

In conclusion, the correct expression that is $\frac{1}{2}$ as large as $486-466$ is $\frac{1}{2}(486-466)$. This expression represents an expression that is proportional to the result of $486-466$, where the multiple is $\frac{1}{2}$.
Frequently Asked Questions (FAQs) About the Expression $\frac{1}{2}$ as Large as $486-466$

Q: What is the concept of proportionality in mathematics?

A: Proportionality is a fundamental concept in mathematics that describes the relationship between two quantities. In this case, we're looking for an expression that is proportional to the result of $486-466$, where the multiple is $\frac{1}{2}$.

Q: How do I determine if an expression is proportional to another?

A: To determine if an expression is proportional to another, you need to check if the expression is a multiple of the other. In this case, we're looking for an expression that is $\frac{1}{2}$ as large as $486-466$, which means the expression should be a multiple of $486-466$ with a multiple of $\frac{1}{2}$.

Q: What is the difference between multiplying and dividing by a fraction?

A: Multiplying by a fraction reduces the value of the expression, while dividing by a fraction increases the value of the expression. In this case, we're looking for an expression that is $\frac{1}{2}$ as large as $486-466$, which means we need to divide the result by $2$, not multiply it.

Q: Can I use the distributive property to simplify the expression?

A: Yes, you can use the distributive property to simplify the expression. However, in this case, we're looking for an expression that is $\frac{1}{2}$ as large as $486-466$, which means we need to divide the result by $2$, not multiply it.

Q: How do I evaluate the expression $\frac{1}{2}(486-466)$?

A: To evaluate the expression, you need to follow the order of operations (PEMDAS):

1. Evaluate the expression inside the parentheses: $486-466 = 20$
2. Multiply the result by $\frac{1}{2}$: $\frac{1}{2} \times 20 = 10$

Q: What is the final answer to the expression $\frac{1}{2}$ as large as $486-466$?

A: The final answer to the expression is $\boxed{10}$.

Q: Can I use a calculator to evaluate the expression?

A: Yes, you can use a calculator to evaluate the expression. However, it's always a good idea to follow the order of operations (PEMDAS) and simplify the expression manually to ensure accuracy.

Q: What is the significance of the expression $\frac{1}{2}$ as large as $486-466$?

A: The expression $\frac{1}{2}$ as large as $486-466$ is a simple example of proportionality in mathematics. It demonstrates how to find an expression that is proportional to another, where the multiple is $\frac{1}{2}$. This concept is essential in various mathematical applications, such as finance, science, and engineering.

Q: Can I apply the concept of proportionality to other mathematical expressions?

A: Yes, you can apply the concept of proportionality to other mathematical expressions. For example, if you have an expression that is $3$ times larger than another, you can find the expression that is $\frac{1}{3}$ as large as the other by dividing the result by $3$.