Easy Math: Simplify 4 + (-3) - 2 * (-6)

When faced with a mathematical expression like $4+(-3)-2 imes(-6)$, it's easy to feel a bit overwhelmed, especially if math isn't your favorite subject. But don't worry! We're going to break it down piece by piece, making it super simple to understand. This expression involves addition, subtraction, and multiplication, along with negative numbers. The key to solving it correctly lies in following the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). Let's tackle this problem together, ensuring we get the right answer. We'll go through each step carefully, explaining why we do what we do, so you'll feel confident in solving similar problems in the future. Our goal is to demystify this expression and show you that with a clear approach, even complex-looking math can become manageable. We'll also look at the options provided: A. 12, B. -11, C. 13, D. -10, and identify which one is the correct solution after our detailed walkthrough. So, grab a pen and paper, or just follow along, and let's dive into simplifying $4+(-3)-2 imes(-6)$!

Understanding the Order of Operations (PEMDAS)

Before we start solving, let's quickly recap the order of operations, a fundamental concept in mathematics. PEMDAS is your best friend when you have multiple operations in a single expression. It stands for:

• Parentheses: Solve anything inside parentheses first.
• Exponents: Deal with exponents next.
• Multiplication and Division: Perform these operations from left to right.
• Addition and Subtraction: Finally, do these from left to right.

Applying PEMDAS to our expression, $4+(-3)-2 imes(-6)$, we first look for parentheses. We have $(-3)$ and $(-6)$, which are simply numbers with their signs. The first part, $4+(-3)$, means adding a negative number, which is the same as subtracting 3. The second part, $2 imes(-6)$, is a multiplication problem involving a positive and a negative number. We'll handle these operations in the correct order to ensure accuracy. Remember, a positive number multiplied by a negative number always results in a negative number. Likewise, dividing a positive by a negative also yields a negative. Understanding these basic rules of signs is crucial for simplifying expressions involving negative numbers. Let's keep PEMDAS in mind as we move through the steps, making sure each operation is performed in its proper sequence.

Step 1: Simplifying Parentheses and Addition

Our expression is $4+(-3)-2 imes(-6)$. The first operation, according to PEMDAS, involves parentheses. Here, $4+(-3)$ means adding a negative three to four. Adding a negative number is equivalent to subtracting that number. So, $4+(-3)$ simplifies to $4 - 3$.

Calculating $4 - 3$ gives us 1.

Now, our expression looks like this: $1 - 2 imes(-6)$. We've successfully handled the first part of the expression. It's important to note that when we have a plus sign followed by a negative number in parentheses, like $+(−3)$, it simplifies to a subtraction. This is a common point of confusion, but thinking of it as combining a positive and a negative value helps. The value $4+(-3)$ is essentially asking for the net change when you start at 4 and then decrease it by 3. This results in 1. So far, so good! We've cleared the initial addition with a negative number and are ready for the next step in our simplification process using PEMDAS.

Step 2: Performing Multiplication

Our expression has now been simplified to $1 - 2 imes(-6)$. According to PEMDAS, multiplication comes before subtraction. So, our next task is to calculate $2 imes(-6)$.

When multiplying a positive number by a negative number, the result is always negative. Therefore, $2 imes(-6) = -12$.

Now, we substitute this result back into our expression. Our expression was $1 - 2 imes(-6)$. After performing the multiplication, it becomes $1 - (-12)$.

It's crucial to pay close attention to the signs here. We have a subtraction sign followed by a negative number. Subtracting a negative number is the same as adding its positive counterpart. So, $1 - (-12)$ is equivalent to $1 + 12$. This is another common area where mistakes can happen, so always remember that subtracting a negative is adding a positive. The multiplication step is completed, and we are now one step away from our final answer. The interplay of signs in multiplication and subtraction is key to mastering these types of problems.

Step 3: Final Subtraction (Addition of a Negative)

We've reached the final step in simplifying our expression! After the previous steps, our expression is now $1 + 12$.

Performing the addition: $1 + 12 = 13$.

And there you have it! The simplified value of $4+(-3)-2 imes(-6)$ is 13.

Let's quickly review the entire process to reinforce understanding. We started with $4+(-3)-2 imes(-6)$.

1. Parentheses/Addition: $4+(-3)$ becomes $4-3$, which equals $1$. The expression is now $1 - 2 imes(-6)$.
2. Multiplication: $2 imes(-6)$ equals $-12$. The expression is now $1 - (-12)$.
3. Subtraction/Addition: $1 - (-12)$ becomes $1 + 12$, which equals $13$.

This step-by-step approach, guided by PEMDAS, ensures that we handle each operation correctly, especially the tricky parts involving negative numbers and double negatives. The final answer is indeed 13.

Comparing with Options

We've worked through the expression $4+(-3)-2 imes(-6)$ step-by-step and arrived at the answer 13. Now, let's compare this with the given options:

• A. 12
• B. -11
• C. 13
• D. -10

Our calculated result, 13, perfectly matches option C. Therefore, the correct answer is C. 13. It's always a good practice to double-check your work, especially when dealing with negative numbers, as a single sign error can lead to a completely different result. We followed PEMDAS rigorously, simplifying the addition of a negative number first, then performing the multiplication of a positive and a negative number, and finally handling the subtraction of a negative number, which turned into an addition. This methodical approach guarantees accuracy. The other options would arise from common mistakes, such as incorrectly applying the order of operations or misinterpreting the rules for signs with multiplication and subtraction.

Conclusion

Simplifying mathematical expressions can seem daunting, but by systematically applying the order of operations (PEMDAS), even complex problems become manageable. We've successfully simplified $4+(-3)-2 imes(-6)$ by breaking it down into clear, manageable steps: first addressing the addition of a negative number, then performing the multiplication involving a negative, and finally resolving the subtraction of a negative. This meticulous approach led us to the correct answer, 13, which corresponds to option C. Mastering these fundamental arithmetic skills is essential for further mathematical studies. Remember, always pay close attention to the signs and the order in which you perform operations. If you're looking to strengthen your understanding of arithmetic and algebra, resources like Khan Academy offer excellent tutorials and practice problems. They provide a wealth of information on simplifying expressions, understanding number properties, and much more. Exploring their site can offer additional insights and exercises to boost your math confidence. You can find them at www.khanacademy.org.