Evaluating 2-(-4)+(-y) When Y=7 A Step-by-Step Guide

In this article, we'll walk through the process of evaluating the expression $2-(-4)+(-y)$ when $y=7$. It might seem a bit daunting at first, but don't worry, we'll break it down step by step, making it super easy to understand. We'll cover the basics of mathematical operations, how to handle negative numbers, and finally, how to substitute a variable's value to get the final answer. So, grab a pen and paper, and let's dive in!

Understanding the Basics: Order of Operations

Before we jump into the main problem, let's quickly recap the order of operations. In mathematics, there's a specific order we need to follow to ensure we get the correct answer. It's often remembered by the acronym PEMDAS, which stands for:

• Parentheses (or brackets)
• Exponents (or powers)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

This order is crucial because it tells us which operations to perform first. For example, in the expression $2 + 3 * 4$, we need to do the multiplication ($3 * 4$) before the addition. If we did the addition first, we'd get a different (and incorrect) answer. Understanding PEMDAS is the first step in successfully evaluating mathematical expressions.

Dealing with Negative Numbers: A Quick Guide

Now, let's talk about negative numbers. These can sometimes be tricky, but with a few simple rules, they become much easier to handle. Remember these key points:

1. Subtracting a negative number is the same as adding a positive number. For example, $5 - (-2)$ is the same as $5 + 2$, which equals 7.
2. Adding a negative number is the same as subtracting a positive number. For example, $5 + (-2)$ is the same as $5 - 2$, which equals 3.
3. The product or quotient of two negative numbers is positive. For example, $(-3) * (-4) = 12$ and $(-10) / (-2) = 5$.
4. The product or quotient of a positive and a negative number is negative. For example, $(-3) * 4 = -12$ and $10 / (-2) = -5$.

These rules are essential for working with expressions that involve negative numbers. Keep them in mind as we tackle our main problem!

Step-by-Step Evaluation of 2-(-4)+(-y) when y=7

Alright, let's get to the heart of the matter! We need to evaluate the expression $2-(-4)+(-y)$ when $y=7$. This means we're going to replace the variable $y$ with the number 7 and then simplify the expression using the order of operations we just discussed.

Step 1: Substitute the value of y

The first thing we need to do is substitute $y$ with 7 in the expression. So, wherever we see $y$, we'll replace it with 7. This gives us:

$2 - (-4) + (-7)$

See? It's just a straightforward replacement. Now we have a numerical expression that we can simplify.

Step 2: Simplify the expression

Now comes the fun part: simplifying! Remember our rules for negative numbers? We'll use those here.

First, let's deal with $2 - (-4)$. As we learned earlier, subtracting a negative number is the same as adding a positive number. So, $2 - (-4)$ becomes $2 + 4$, which equals 6. Our expression now looks like this:

$6 + (-7)$

Next, we have $6 + (-7)$. Adding a negative number is the same as subtracting a positive number. So, $6 + (-7)$ is the same as $6 - 7$. Can you guess the answer?

$6 - 7 = -1$

And there you have it! We've simplified the expression. So, $2-(-4)+(-y)$ when $y=7$ equals -1.

Alternative Explanation

Some of you might find it helpful to see this explained in another way. Let's break down each part of the expression:

• $2$ is just 2. No changes needed here.
• $-(-4)$ means the opposite of -4, which is +4. So, this part becomes +4.
• $(-y)$ when $y=7$ means the opposite of 7, which is -7. So, this part becomes -7.

Now, we can rewrite the expression as:

$2 + 4 + (-7)$

Adding the positive numbers first, we get $2 + 4 = 6$. So, the expression becomes:

$6 + (-7)$

And as we discussed before, $6 + (-7)$ is the same as $6 - 7$, which equals -1. We arrived at the same answer, just with a slightly different way of thinking about it!

Common Mistakes to Avoid

When evaluating expressions like this, there are a few common mistakes that people often make. Knowing these pitfalls can help you avoid them and get the correct answer every time.

1. Forgetting the order of operations: This is a big one! If you don't follow PEMDAS, you're likely to end up with the wrong answer. Always remember to do parentheses and exponents first, then multiplication and division, and finally, addition and subtraction.
2. Misunderstanding negative numbers: Negative numbers can be tricky if you don't remember the rules. Make sure you understand that subtracting a negative is the same as adding a positive, and adding a negative is the same as subtracting a positive.
3. Incorrectly substituting the value of the variable: When substituting a variable, make sure you replace it correctly. It's easy to make a mistake if you're rushing, so take your time and double-check your work.
4. Arithmetic errors: Simple arithmetic mistakes can happen to anyone, especially when working with negative numbers. Always double-check your calculations to make sure you haven't made any errors.

By being aware of these common mistakes, you can significantly reduce your chances of making them and improve your accuracy.

Practice Problems: Test Your Understanding

Now that we've walked through the process, it's time to put your knowledge to the test! Here are a few practice problems for you to try. Remember to use the order of operations and the rules for negative numbers.

1. Evaluate $5 - (-3) + (-x)$ when $x = 4$
2. Evaluate $-2 + (-6) - (-y)$ when $y = 8$
3. Evaluate $10 - (-2) + (-z)$ when $z = 5$

Try solving these on your own, and then check your answers. Practice is key to mastering these concepts!

Real-World Applications of Evaluating Expressions

You might be wondering,