Solving: 24 – 2 × 5 + 3. A Step-by-Step Guide

by Dimemap Team 46 views

Alright, guys, let's dive into solving this math problem together! We're going to break down the expression 24 – 2 × 5 + 3 step by step, making sure we get the correct answer. Math can seem tricky sometimes, but with a clear approach, it becomes much easier. So, grab your pencils, and let's get started!

Understanding the Order of Operations

Before we even touch the numbers, we need to understand the order of operations. This is a set of rules that tells us which operations (like multiplication, addition, etc.) to do first. Remember PEMDAS/BODMAS? It stands for:

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

Following this order is super important because doing operations in the wrong order will lead to the wrong answer. In our problem, 24 – 2 × 5 + 3, we have subtraction, multiplication, and addition. According to PEMDAS/BODMAS, we need to do the multiplication first.

Step 1: Multiplication

The first thing we're going to tackle is the multiplication part of the expression: 2 × 5. This is straightforward:

2 × 5 = 10

Now, we can rewrite the original expression with this result. So, 24 – 2 × 5 + 3 becomes 24 – 10 + 3. See how we've simplified it already? This is how we make complex problems manageable—by breaking them down into smaller, easier steps.

Step 2: Subtraction

Next up, we have subtraction and addition. According to the order of operations, we perform these from left to right. So, we start with the subtraction: 24 – 10. Let's calculate that:

24 – 10 = 14

Now our expression looks even simpler: 14 + 3. We're almost there!

Step 3: Addition

Finally, we perform the addition: 14 + 3. This is the last step, and it will give us our final answer:

14 + 3 = 17

So, the final result of the expression 24 – 2 × 5 + 3 is 17. Woo-hoo! We did it!

Let's Recap

To make sure we've got it all down, let's quickly recap the steps we took:

  1. Identify the operations: We recognized that we had subtraction, multiplication, and addition.
  2. Follow the order of operations: We remembered PEMDAS/BODMAS and knew to do multiplication before addition and subtraction.
  3. Multiply: We calculated 2 × 5 = 10.
  4. Rewrite the expression: We rewrote the expression as 24 – 10 + 3.
  5. Subtract: We subtracted 24 – 10 = 14.
  6. Add: We added 14 + 3 = 17.
  7. Final Answer: Therefore, 24 – 2 × 5 + 3 = 17.

By following these steps carefully, we arrived at the correct answer. Remember, the key is to take your time and break the problem down into smaller, manageable parts. With a little practice, you'll become a pro at solving these kinds of expressions!

Why Is the Order of Operations Important?

You might be wondering, why all the fuss about the order of operations? Well, imagine if we didn't follow these rules. If we just went from left to right, we'd do 24 – 2 first, which equals 22. Then we'd multiply 22 × 5, getting 110, and finally add 3 to get 113. That's a completely different answer! The order of operations ensures that everyone gets the same, correct answer by following the same rules. It brings consistency and clarity to math, making it possible for us to solve complex problems accurately.

Real-World Applications

Understanding the order of operations isn't just useful for math class. It also has real-world applications. For example, when you're calculating expenses or figuring out a budget, you need to perform operations in the correct order to get an accurate result. Imagine you're buying groceries. You have a coupon that takes $5 off your total bill, and then there's a 10% sales tax. To calculate your final cost correctly, you need to subtract the coupon amount before calculating the sales tax. This is just one example of how the order of operations is used in everyday life. It's a fundamental concept that helps us make accurate calculations and informed decisions.

Practice Makes Perfect

The best way to master the order of operations is to practice. Try solving different expressions with varying operations and levels of complexity. Start with simple expressions and gradually move on to more challenging ones. You can find plenty of practice problems online or in math textbooks. As you practice, pay close attention to the order of operations and make sure you're following the rules correctly. Don't be afraid to make mistakes—they're a natural part of the learning process. When you do make a mistake, take the time to understand why you made it and how you can avoid making it again in the future. With consistent practice, you'll build confidence and improve your skills.

Tips and Tricks

Here are a few tips and tricks to help you master the order of operations:

  • Write it out: When you're solving an expression, write out each step clearly. This will help you keep track of what you're doing and avoid making mistakes.
  • Use parentheses: If you're not sure about the order of operations, use parentheses to group operations together. This will make it clear which operations should be performed first.
  • Check your work: After you've solved an expression, take a moment to check your work. Make sure you've followed the order of operations correctly and that your calculations are accurate.
  • Ask for help: If you're struggling with the order of operations, don't be afraid to ask for help. Talk to your teacher, a tutor, or a friend who's good at math. They can provide you with additional guidance and support.

Common Mistakes to Avoid

When working with the order of operations, there are a few common mistakes that you should try to avoid:

  • Forgetting PEMDAS/BODMAS: Always remember the order of operations (PEMDAS/BODMAS) and follow it carefully. This is the most important rule to remember.
  • Skipping steps: Don't try to skip steps or do too much in your head. Write out each step clearly to avoid making mistakes.
  • Ignoring signs: Pay close attention to the signs of the numbers (positive or negative). A simple sign error can throw off your entire calculation.
  • Not checking your work: Always check your work after you've solved an expression. This will help you catch any mistakes you may have made.

Conclusion

So, there you have it! Solving the expression 24 – 2 × 5 + 3 involves understanding and applying the order of operations. By following PEMDAS/BODMAS, we first perform the multiplication, then the subtraction, and finally the addition, leading us to the correct answer of 17. Remember, practice makes perfect, so keep working on similar problems to sharpen your skills. Math might seem daunting at times, but with a clear understanding and a step-by-step approach, you can conquer any problem that comes your way. Keep up the great work, and happy calculating!

Now you guys know how to solve such problems. Keep practicing and you'll become a math whiz in no time! You got this!