Simplifying 11 - [4 + 2 * 3] A Step-by-Step Guide

Have you ever stared at a mathematical expression and felt a little overwhelmed? Don't worry, guys, we've all been there! Math can sometimes look intimidating, but with the right approach, even the most complex problems can be broken down into simpler steps. In this guide, we're going to tackle the expression 11 - [4 + 2 ⋅ 3] together. We'll walk through each step, explain the logic behind it, and by the end, you'll feel like a math whiz!

Understanding the Order of Operations

Before we dive into the specifics of our expression, it's crucial to understand the order of operations. This is the golden rule of mathematics that tells us in what sequence we should perform calculations to get the correct answer. Think of it as the recipe for solving mathematical expressions. The order of operations is often remembered by the acronym PEMDAS, which stands for:

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

So, what does this mean for our expression? It means we need to tackle the operations within the brackets first, paying special attention to multiplication before addition. Ignoring this order can lead to drastically different and incorrect answers. Trust me, following PEMDAS is your best friend in the world of math!

Step-by-Step Breakdown of 11 - [4 + 2 ⋅ 3]

Now, let's get our hands dirty and solve the expression step-by-step. We'll break it down so it’s super clear and easy to follow. Remember, our expression is:

11 - [4 + 2 ⋅ 3]

Step 1: Focus on the Parentheses (Brackets)

The first thing we need to do, according to PEMDAS, is to deal with the expression inside the brackets: [4 + 2 ⋅ 3]. This is where we apply the order of operations again, but just within the brackets. Inside the brackets, we have both addition and multiplication. Which one comes first? You guessed it – multiplication!

Step 2: Perform the Multiplication

Within the brackets, we have 2 ⋅ 3, which means 2 multiplied by 3. This gives us 6. So now, we can rewrite the expression within the brackets as:

[4 + 6]

See how we're simplifying things bit by bit? It’s like decluttering a room – one step at a time!

Step 3: Complete the Addition within the Brackets

Now that we've taken care of the multiplication, we can perform the addition inside the brackets. We have 4 + 6, which equals 10. So, the expression within the brackets simplifies to:

10

Our original expression now looks much simpler:

11 - 10

Step 4: Perform the Subtraction

We're in the home stretch! The final step is to perform the subtraction. We have 11 - 10, which equals 1. So, the final simplified answer is:

1

And there you have it! We've successfully simplified the expression 11 - [4 + 2 ⋅ 3] to 1. Pat yourselves on the back, guys – you've earned it!

Common Mistakes to Avoid

Before we celebrate too much, let's talk about some common pitfalls people stumble into when solving expressions like this. Being aware of these mistakes can save you a lot of headaches (and incorrect answers) in the future.

Mistake 1: Ignoring the Order of Operations

This is the biggest culprit. Many people might be tempted to perform the addition before the multiplication within the brackets. For example, they might calculate 4 + 2 first, getting 6, and then multiply by 3, getting 18. This would lead to a completely different (and wrong) answer. Remember, PEMDAS is your mantra! Always multiply before adding within parentheses.

Mistake 2: Misunderstanding Brackets and Parentheses

Brackets and parentheses are grouping symbols, and they tell us to prioritize the operations inside them. It's crucial to handle everything inside the brackets before moving on to the rest of the expression. Think of them as VIP areas in a math problem – you need to deal with what's inside before you can move on to the general crowd.

Mistake 3: Arithmetic Errors

Sometimes, the mistake isn't about the order of operations but simply making a small arithmetic error, like adding or multiplying incorrectly. This is why it's always a good idea to double-check your calculations, especially in longer expressions. Even a tiny slip-up can throw off the entire answer.

Mistake 4: Not Rewriting the Expression

As we showed in our step-by-step breakdown, rewriting the expression after each operation makes it much easier to keep track of what you've done and what still needs to be done. Trying to do everything in your head is a recipe for disaster (or at least a higher chance of making a mistake). Take the time to rewrite – it's worth it!

Practice Makes Perfect

The best way to become a math master is to practice, practice, practice! Try simplifying similar expressions on your own. The more you practice, the more comfortable you'll become with the order of operations and the less likely you'll be to make mistakes. Here are a few practice problems to get you started:

1. 15 - [3 + 4 ⋅ 2]
2. 20 + [10 - 2 ⋅ 3]
3. 8 ⋅ [5 - 1 + 2]

Work through these problems, and feel free to check your answers with a calculator. But remember, the goal is not just to get the right answer, but to understand the process. So, show your work, break down each step, and you'll be well on your way to math success!

Conclusion: Mastering Mathematical Expressions

Simplifying mathematical expressions might seem daunting at first, but as we've seen with 11 - [4 + 2 ⋅ 3], it's all about breaking down the problem into manageable steps and following the order of operations. PEMDAS is your friend, and with practice, you'll be able to tackle even the trickiest expressions with confidence. So, keep practicing, stay curious, and remember that every math problem is just a puzzle waiting to be solved. You've got this, guys!