Evaluating -3.28-(-4.4)+(-p) Where P=9.7 A Step-by-Step Guide

Hey guys! Today, we're diving into a fun little math problem where we need to evaluate an expression involving decimals and a variable. Don't worry, it's not as scary as it looks! We'll break it down step by step so it's super easy to follow. Our mission, should we choose to accept it (and we do!), is to figure out the value of the expression $-3.28-(-4.4)+(-p)$ when $p$ is equal to $9.7$. So, grab your calculators (or your mental math muscles) and let's get started!

Breaking Down the Expression

Let's first understand the key components of the expression. The expression we're tackling is $-3.28-(-4.4)+(-p)$. This involves a few things we need to keep in mind: negative numbers, subtraction of a negative number, and addition of a negative number. These are the building blocks of our problem, and understanding them is crucial. Let’s delve deeper into each of these components to ensure we're all on the same page before we start plugging in numbers and crunching calculations.

Understanding Negative Numbers

First off, let's talk about negative numbers. Negative numbers are numbers less than zero, and they're used all the time in real life – think about temperatures below zero or owing money. In our expression, we see $-3.28$ and $-4.4$. The minus sign in front of these numbers indicates that they are negative. It's like saying we're $3.28$ units to the left of zero on the number line, or $4.4$ units in debt. Grasping this concept is fundamental to working with expressions like ours. Negative numbers might seem a bit tricky at first, but with a bit of practice, they'll become second nature. Remember, they're just the flip side of the positive numbers we're already familiar with!

Subtracting a Negative Number

Now, let's tackle the concept of subtracting a negative number. This is where things can get a little bit mind-bending, but I promise it's not as complicated as it seems. When we see $-(-4.4)$ in our expression, it means we're subtracting a negative number. The golden rule here is that subtracting a negative number is the same as adding its positive counterpart. So, $-(-4.4)$ is the same as $+4.4$. Think of it like this: taking away a debt is like gaining money. This concept is super important, and it's one of the most common places where people make mistakes, so make sure you've got it down pat. Mastering this will make a huge difference in your ability to handle mathematical expressions confidently.

Adding a Negative Number

Finally, we have the addition of a negative number, represented by $+(-p)$ in our expression. This is a bit more straightforward. Adding a negative number is the same as simply subtracting that number. So, $+(-p)$ is the same as $-p$. Imagine you're adding a debt to your account; it's the same as reducing your balance. This rule is crucial for simplifying expressions and avoiding confusion. It's all about understanding that the plus and minus signs have a big impact on the outcome, and knowing how to handle them is key to success in math. So, let’s keep this in mind as we move forward!

Plugging in the Value of p

Now that we've dissected the expression and understand all its components, it's time to bring in the value of $p$. We're told that $p = 9.7$, so we need to substitute this value into our expression. Replacing $p$ with $9.7$ gives us $-3.28 - (-4.4) + (-9.7)$. See how we've simply swapped out the variable $p$ for its numerical value? This is a fundamental step in solving algebraic expressions, and it's something you'll do time and time again in math. It's like translating a sentence from one language to another; we're taking the symbolic representation ($p$) and turning it into its concrete numerical equivalent ($9.7$). This substitution is the bridge between the abstract world of variables and the concrete world of numbers, so let’s make sure we do it right!

Simplifying the Expression

With $p$ replaced, our expression now looks like a string of numbers and operations, ready to be simplified. The next step is to tackle those minus signs and additions. Remember our earlier discussion about subtracting a negative number? $-(-4.4)$ becomes $+4.4$. And adding a negative number, like $+(-9.7)$, is the same as subtracting, so it becomes $-9.7$. Our expression morphs into $-3.28 + 4.4 - 9.7$. This transformation is crucial because it turns a potentially confusing string of operations into a more manageable one. By applying these rules, we're essentially cleaning up the expression, making it easier to see the path to the solution. It's like decluttering a room; once you've organized things, it's much easier to find what you're looking for. So, let’s proceed with this simplified expression and move towards the final calculation!

Performing the Calculation

Alright, guys, it's calculation time! We've got our simplified expression: $-3.28 + 4.4 - 9.7$. Now, we just need to do the arithmetic. It's often easiest to work from left to right, but remember, addition and subtraction are commutative, meaning we can change the order if it makes things simpler. Let's start by adding $-3.28$ and $4.4$. If you think of this in terms of money, it's like having a debt of $3.28 and then gaining $4.4. The result is $1.12$. So now our expression looks like $1.12 - 9.7$. Next, we subtract $9.7$ from $1.12$. This is like having $1.12 and then spending $9.7; you're going to end up in debt. The final result is $-8.58$. And there we have it! We've successfully navigated the expression and arrived at our final answer. Remember, math is all about breaking things down into manageable steps, and we've done exactly that here.

The Final Answer

So, after all that simplification and calculation, we've arrived at the final answer! The value of the expression $-3.28-(-4.4)+(-p)$ when $p=9.7$ is $\boxed{-8.58}$. Awesome job, guys! You've tackled negative numbers, subtracted negatives, and plugged in variables like pros. Remember, practice makes perfect, so the more you work with these kinds of problems, the easier they'll become. Keep up the great work, and you'll be math masters in no time!

This wasn't so bad, was it? Math can be a bit like a puzzle, and we just solved this one together. The key is to break it down into smaller steps, understand the rules, and take your time. You've got this!