Next Step: Evaluating 90 - (18 + -2)(-3) Expression

Hey guys! Ever find yourself staring at a math problem that looks like a jumbled mess of numbers and operations? Don't worry; we've all been there! Today, we're going to break down a specific type of problem: evaluating numerical expressions. Specifically, we'll tackle the expression 90 - (18 + -2)(-3) and figure out the next step after we've simplified the parentheses. So, grab your pencils, and let's dive in!

Understanding the Order of Operations

Before we jump into the problem, let's quickly refresh our memory about the order of operations. This is the golden rule that tells us the sequence in which we should perform calculations. You might have heard of the acronym PEMDAS, which stands for:

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

Think of PEMDAS as your mathematical GPS, guiding you through the maze of numbers and symbols. It ensures that everyone arrives at the same answer, no matter who's doing the calculating. Ignoring PEMDAS can lead to chaos and incorrect results, so it's super important to stick to it!

When dealing with expressions involving multiple operations, remembering PEMDAS is crucial for obtaining the correct answer. For instance, consider the expression 2 + 3 * 4. If we perform the addition first, we get 5 * 4 = 20. However, according to PEMDAS, we should perform multiplication before addition, which gives us 2 + 12 = 14. See the difference? Following the order of operations ensures we arrive at the accurate solution.

Breaking Down the Expression: 90 - (18 + -2)(-3)

Now, let's get back to our expression: 90 - (18 + -2)(-3). Geno has already started evaluating it, and the first step he took was to simplify inside the parentheses. Let's follow along with his progress:

1. Original Expression: 90 - (18 + -2)(-3)
2. Simplify Parentheses: 90 - (16)(-3)

Great job, Geno! He correctly simplified 18 + -2 to 16. So, what's the next move? Looking at our expression 90 - (16)(-3), we need to figure out which operation comes next according to PEMDAS.

Remember PEMDAS? We've already taken care of the P (Parentheses). There are no Exponents in this expression, so we move on to Multiplication and Division. We see a multiplication operation: (16)(-3). This is our next target!

Why is multiplication the next step? Well, after dealing with parentheses, PEMDAS tells us to handle multiplication and division before we tackle addition and subtraction. In our expression, the multiplication is lurking inside the second term, so we need to deal with it before we can think about the subtraction.

The Next Step: Multiplication

So, the next step Geno should take is to perform the multiplication: (16)(-3). Let's do that:

16 * -3 = -48

Now our expression looks like this:

90 - (-48)

Notice how we've replaced (16)(-3) with its result, -48. We're making progress towards simplifying the entire expression! Understanding the sign rules in multiplication is essential here. Remember, a positive number multiplied by a negative number results in a negative number.

Final Steps: Subtraction and the Importance of Sign Rules

We're almost there! Our expression is now 90 - (-48). According to PEMDAS, the final operation we need to perform is Subtraction. But wait, there's a sneaky double negative in there! Remember that subtracting a negative number is the same as adding a positive number. So, we can rewrite our expression as:

90 + 48

Now it's a simple addition problem:

90 + 48 = 138

And that's our final answer! Geno's expression, 90 - (18 + -2)(-3), evaluates to 138. See how following the order of operations step-by-step helped us reach the solution? Getting those sign rules right is also super important, as a small mistake there can throw off your entire calculation.

Key Takeaways for Evaluating Expressions

Let's recap the key takeaways from this problem:

1. PEMDAS is your friend: Always follow the order of operations (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to ensure accurate calculations.
2. Simplify inside parentheses first: This is usually the starting point for evaluating expressions.
3. Multiplication and Division before Addition and Subtraction: These operations take precedence according to PEMDAS.
4. Watch out for sign rules: Pay close attention to positive and negative signs, especially when multiplying and subtracting.
5. Break it down step-by-step: Complex expressions can be intimidating, but breaking them down into smaller, manageable steps makes the process much easier.

Practice Makes Perfect

Evaluating numerical expressions might seem tricky at first, but with practice, you'll become a pro in no time! The more you work through different problems, the more comfortable you'll become with the order of operations and the various mathematical rules involved. So, don't be afraid to tackle those expressions head-on!

To level up your skills, try working through various examples. Start with simpler expressions and gradually move on to more complex ones. Challenge yourself to identify the correct order of operations and pay close attention to the signs of the numbers. You'll be surprised at how quickly you improve with consistent practice.

Conclusion: Mastering the Order of Operations

So, there you have it! We've successfully navigated the expression 90 - (18 + -2)(-3) and figured out the next step after simplifying the parentheses. Remember, the key is to follow the order of operations (PEMDAS) and take it one step at a time. Keep practicing, and you'll become a master of evaluating numerical expressions. Now go forth and conquer those math problems!

Math can be challenging, but it can also be incredibly rewarding. By understanding the fundamental rules and practicing regularly, you can build your confidence and tackle even the most complex problems. So, keep exploring, keep learning, and keep having fun with math!