Understanding 8 × 4 - 2: Which Descriptions Match?

Hey guys! Let's dive into understanding the mathematical expression 8 × 4 - 2. It's super important to know how to correctly interpret these kinds of expressions, and we're going to break it down in a way that's easy to grasp. We'll go through each option, see what it means, and figure out which ones match our expression. So, let's get started!

Breaking Down the Expression

First off, let's talk about the order of operations. You've probably heard of PEMDAS/BODMAS, right? It's the golden rule for solving math problems! It tells us the order we need to follow: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). So, for our expression 8 × 4 - 2, we need to do the multiplication first and then the subtraction.

• Multiplication: We start by multiplying 8 and 4. 8 × 4 equals 32.
• Subtraction: Next, we subtract 2 from the result. 32 - 2 equals 30.

So, the value of the expression 8 × 4 - 2 is 30. Now that we know this, we can check which descriptions match this calculation. It's like we're math detectives, matching clues to the right answer!

Evaluating the Descriptions

Okay, let's put on our detective hats and go through each description to see if it matches our expression 8 × 4 - 2. We're looking for the descriptions that accurately represent the steps we just took: multiply 8 by 4, and then subtract 2. Let's break down each option and see if it fits the bill. Remember, it's all about understanding the words and how they translate into math!

Option A: 8 times the difference of 4 and 2

This option, “8 times the difference of 4 and 2,” sounds a bit tricky, right? It's super crucial to break it down carefully. The phrase "the difference of 4 and 2" means we need to subtract 2 from 4 first. So, in math terms, that's 4 - 2. And then, we're supposed to multiply the result by 8. This translates to the expression 8 × (4 - 2). Notice those parentheses? They're super important because they change the order of operations. Without them, we'd be doing something completely different!

So, let's work it out: 4 - 2 equals 2, and then 8 × 2 equals 16. This means the value of the expression 8 × (4 - 2) is 16. Now, remember our original expression, 8 × 4 - 2, which equals 30. Are 16 and 30 the same? Nope! So, Option A doesn't match our expression. It's a good reminder that even small changes in wording can completely change the math. It’s all about paying attention to those details, guys!

Option B: Multiply 8 and 4, then subtract 2

Now, let's tackle Option B: “Multiply 8 and 4, then subtract 2.” This one sounds pretty straightforward, doesn't it? It’s like it’s laying out the steps nice and clear for us. The first part says we need to multiply 8 and 4. So, that's 8 × 4. Easy peasy! The second part tells us to subtract 2 from the result. So, we take whatever we get from 8 × 4 and then subtract 2. In math terms, that’s exactly what our original expression, 8 × 4 - 2, does!

Let's double-check: 8 × 4 is 32, and then subtracting 2 gives us 30. This is exactly the same value we got when we calculated 8 × 4 - 2 earlier. So, guess what? Option B matches our expression perfectly! It’s like finding the perfect puzzle piece. This option directly reflects the order of operations we need to follow, making it a clear and correct description. We’re on a roll, guys!

Option C: 2 less than the product of 8 and 4

Alright, let’s dive into Option C: “2 less than the product of 8 and 4.” This one uses a bit of tricky wording, so we need to unpack it carefully. When we see “the product of 8 and 4,” what does that mean? It means we need to multiply 8 and 4. So, we’ve got 8 × 4. Now, the phrase “2 less than” is super important. It tells us that we need to subtract 2 from something. But from what? From the product of 8 and 4!

So, we take the result of 8 × 4 and then subtract 2. This gives us the expression (8 × 4) - 2. Notice that the parentheses here aren't strictly necessary because the order of operations already tells us to do the multiplication before the subtraction. But they can help make it clearer! Now, let’s calculate: 8 × 4 is 32, and then 32 - 2 is 30. Guess what? This is exactly the same as our original expression 8 × 4 - 2!

So, Option C is another match! It’s like we’re building up a collection of correct descriptions. The key here is understanding what “2 less than” means – it’s a common phrase in math problems, and knowing how to translate it is super helpful. We’re doing great, guys!

Option D: Subtract 2 from 4, then multiply by 8

Okay, let’s tackle the final option, Option D: “Subtract 2 from 4, then multiply by 8.” Just like before, we need to break this down step by step to make sure we get it right. The first part of the description says, “Subtract 2 from 4.” What does that mean in math terms? It means we’re doing 4 - 2. Nice and straightforward! The second part says, “then multiply by 8.” So, we take the result of 4 - 2 and multiply it by 8.

This gives us the expression 8 × (4 - 2). Notice those parentheses again? They’re super important because they tell us to do the subtraction before the multiplication. Now, let’s calculate: 4 - 2 equals 2, and then 8 × 2 equals 16. So, the value of this expression is 16. But remember, our original expression 8 × 4 - 2 equals 30. Are 16 and 30 the same? Nope! So, Option D doesn’t match our expression.

This is a great example of how changing the order of operations can completely change the result. We had to pay close attention to the wording to make sure we translated it correctly into a mathematical expression. We're really getting the hang of this, guys!

Final Answer: Which Descriptions Correspond?

Alright, let's recap what we've found. We've gone through each option, broken them down, and compared them to our original expression, 8 × 4 - 2. Remember, the value of 8 × 4 - 2 is 30.

• Option A: "8 times the difference of 4 and 2" – This translates to 8 × (4 - 2), which equals 16. So, it doesn't match.
• Option B: "Multiply 8 and 4, then subtract 2" – This perfectly describes 8 × 4 - 2, which equals 30. So, it matches!
• Option C: "2 less than the product of 8 and 4" – This also translates to (8 × 4) - 2, which equals 30. So, it matches too!
• Option D: "Subtract 2 from 4, then multiply by 8" – This gives us 8 × (4 - 2), which equals 16. So, it doesn't match.

So, the descriptions that correspond to the expression 8 × 4 - 2 are Option B and Option C. We nailed it! This exercise shows how important it is to understand the wording of mathematical descriptions and how they translate into actual expressions. It’s like learning a new language, guys! And we're becoming fluent in math-speak!