Evaluating Expressions Order Of Operations Example

Introduction

Hey guys! Today, we're diving into a fun math problem that involves the order of operations. We'll be evaluating the expression $8 imes [(20 - 10) t{÷} 5 + 1]$. Don't worry; it might look a bit intimidating at first, but we'll break it down step by step. Understanding how to correctly evaluate such expressions is crucial for mastering basic arithmetic and algebra. So, let’s get started and make math enjoyable!

Understanding the Order of Operations

Before we jump into the problem, let's quickly recap the order of operations. This is the golden rule that tells us which operations to perform first in a mathematical expression. Remember PEMDAS, which stands for:

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

Following PEMDAS ensures we always arrive at the correct answer. It's like a recipe – you need to follow the steps in the right order to get the desired result! In our expression, we have parentheses, division, addition, and multiplication, so we’ll need to keep PEMDAS in mind.

Step-by-Step Evaluation

Okay, let’s tackle the expression $8 imes [(20 - 10) t{÷} 5 + 1]$ step by step. We'll go through each operation, explaining what we're doing and why.

Step 1: Parentheses

First up, we need to deal with the parentheses. Inside the brackets, we have $(20 - 10)$. This is a simple subtraction, so let’s do it:

$20 - 10 = 10$

Now our expression looks like this:

$8 imes [10 t{÷} 5 + 1]$

Step 2: Division

Next, we have another set of brackets. Inside these brackets, we have division and addition. According to PEMDAS, we need to do the division first. So, let’s divide 10 by 5:

$10 t{÷} 5 = 2$

Our expression now looks like this:

$8 imes [2 + 1]$

Step 3: Addition

We're still inside the brackets, so we need to finish the operation there. Now we have addition: $2 + 1$:

$2 + 1 = 3$

The expression simplifies to:

$8 imes 3$

Step 4: Multiplication

Finally, we have the multiplication. This is the last operation left, so let’s multiply 8 by 3:

$8 imes 3 = 24$

And there we have it! The value of the expression $8 imes [(20 - 10) t{÷} 5 + 1]$ is 24.

Detailed Breakdown of the Solution

Let’s walk through the entire solution again to make sure we’ve got it crystal clear. This step-by-step approach is super helpful for avoiding mistakes and building confidence.

1. Original Expression: $8 imes [(20 - 10) t{÷} 5 + 1]$
2. Parentheses (Subtraction): $8 imes [10 t{÷} 5 + 1]$
3. Brackets (Division): $8 imes [2 + 1]$
4. Brackets (Addition): $8 imes 3$
5. Multiplication: $24$

So, by carefully following the order of operations, we've successfully evaluated the expression. Remember, the key is to take it one step at a time and stay organized.

Common Mistakes to Avoid

When evaluating expressions, it’s easy to make a few common mistakes. Let's look at some of these so you can steer clear of them:

• Forgetting PEMDAS: This is the biggest pitfall. Always remember the order of operations. If you skip a step or do them in the wrong order, you’ll likely get the wrong answer.
• Incorrectly Simplifying Parentheses: Make sure you complete all operations inside the parentheses before moving on. Sometimes, there can be multiple operations within parentheses, so take it slow and do them one at a time.
• Mixing Up Multiplication and Division or Addition and Subtraction: Remember that multiplication and division have the same priority, so you work from left to right. The same goes for addition and subtraction.
• Rushing: Math isn't a race! Take your time, double-check your work, and make sure each step is correct. A little patience can save you from making errors.

Practice Problems

Now that we've walked through the solution, let’s try a couple of similar problems to help you practice. The best way to master math is by doing it, so grab a pencil and paper, and let’s go!

1. $10 imes [(15 - 5) t{÷} 2 + 3]$
2. $6 + [12 t{÷} (4 - 2)] imes 5$

Work through these problems using the same steps we discussed. Remember PEMDAS, and take your time. The answers are at the end of this article, so you can check your work.

Real-World Applications

You might be wondering,