Solve 40 - 7 × (2²) √10² - 252/7: Step-by-Step Guide

by Viktoria Ivanova 53 views

Hey guys! Let's dive into solving this mathematical expression: 40 - 7 × (2²) √10² - 252/7. It might look intimidating at first, but don't worry! We're going to break it down step by step, making sure everything is crystal clear. So, grab your calculators (or your trusty mental math skills) and let's get started!

Understanding the Order of Operations

Before we jump into the nitty-gritty, it's super important to understand the order of operations. Think of it as the golden rule of math – we gotta follow it to get the correct answer. The order is usually remembered by the acronym PEMDAS, which stands for:

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

Keeping PEMDAS in mind will help us tackle this problem systematically and avoid any confusion. Trust me, it's like having a roadmap for solving mathematical equations!

Step 1: Simplify Parentheses and Exponents

Alright, let's kick things off by tackling the parentheses and exponents in our expression: 40 - 7 × (2²) √10² - 252/7.

Parentheses First!

Inside the parentheses, we have 2², which means 2 raised to the power of 2. This is the same as 2 multiplied by itself: 2 × 2 = 4. So, we can replace (2²) with 4 in our expression. See? We're already making progress!

Exponents Next!

We also have a square root in our expression: √10². The square root of a number squared is simply the number itself. So, √10² = 10. This is a handy little trick to remember, guys. It will save you time in the long run.

Now our expression looks like this: 40 - 7 × 4 × 10 - 252/7. Much cleaner, right? We've handled the parentheses and exponents, and we're ready to move on to the next step.

Remember, focusing on these foundational rules ensures accuracy and helps simplify even the most complex equations. By breaking down each component, you'll find that mathematical problems become far more manageable and less daunting. This initial simplification is key to preventing errors and setting the stage for the subsequent calculations.

Step 2: Perform Multiplication and Division

Now that we've simplified the parentheses and exponents, it's time to tackle multiplication and division. Remember, we do these operations from left to right, just like reading a sentence. Our expression currently looks like this: 40 - 7 × 4 × 10 - 252/7.

Multiplication Operations

First up, we have 7 × 4. This one's pretty straightforward: 7 × 4 = 28. So, we replace 7 × 4 with 28, and our expression becomes 40 - 28 × 10 - 252/7.

Next, we have 28 × 10. Multiplying by 10 is super easy – just add a zero to the end of the number! So, 28 × 10 = 280. Now our expression is looking even simpler: 40 - 280 - 252/7.

Division Operation

Now let's handle the division: 252/7. If you're not sure off the top of your head, you can do a little long division or use a calculator. The answer is 252 / 7 = 36. So, we replace 252/7 with 36, and our expression now reads 40 - 280 - 36.

By meticulously addressing multiplication and division from left to right, we maintain the integrity of the equation and ensure that our final answer will be correct. Each multiplication and division step brings us closer to the solution by unraveling the complexity of the initial expression. Keeping track of each operation is essential for avoiding common mistakes and building confidence in your problem-solving skills.

Step 3: Handle Addition and Subtraction

We're in the home stretch now! The final step is to take care of addition and subtraction. Just like with multiplication and division, we'll work from left to right. Our expression currently looks like this: 40 - 280 - 36.

Subtraction Operations

First, let's do 40 - 280. This might seem a bit tricky because we're subtracting a larger number from a smaller one, which will give us a negative result. 40 - 280 = -240. So, we replace 40 - 280 with -240, and the expression becomes -240 - 36.

Next, we have -240 - 36. This is like adding two negative numbers together. Think of it as owing $240 and then owing another $36. The result is -240 - 36 = -276.

And there we have it! We've simplified the entire expression step by step, and we've arrived at our final answer.

Remember, performing addition and subtraction accurately is the final piece of the puzzle. Working from left to right ensures that no term is missed and that the signs are correctly handled. This careful approach to the last operations solidifies the final result and guarantees that the solution is both precise and reliable. By understanding and applying these steps consistently, you'll become more adept at solving mathematical problems of any complexity.

Final Answer

So, after carefully working through all the steps, we've found that:

40 - 7 × (2²) √10² - 252/7 = -276

Awesome job, guys! We took a seemingly complicated problem and broke it down into manageable steps. By following the order of operations (PEMDAS) and taking our time, we were able to arrive at the correct solution. Math can be fun when you approach it with a clear strategy and a little bit of confidence!

Key Takeaways

Let's recap the key things we learned while solving this problem:

  1. The Order of Operations (PEMDAS): This is the golden rule! Always remember to do Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
  2. Simplifying Exponents and Square Roots: Remember that the square root of a number squared is the number itself (e.g., √10² = 10). This can save you a lot of time and effort.
  3. Working from Left to Right: When you have multiple multiplication/division or addition/subtraction operations, always work from left to right.
  4. Breaking Down Complex Problems: Don't be intimidated by long expressions! Break them down into smaller, more manageable steps. This makes the problem less overwhelming and reduces the chance of making mistakes.
  5. Double-Checking Your Work: It's always a good idea to double-check your calculations, especially when dealing with negative numbers or multiple operations. A small mistake can throw off your entire answer.

By mastering these key takeaways, you'll be well-equipped to tackle a wide range of mathematical problems. Remember, practice makes perfect, so keep challenging yourself and you'll become a math whiz in no time!

Practice Problems

Want to test your skills and solidify your understanding? Try solving these practice problems:

  1. 50 + 3 × (4²) - √81 + 18/3
  2. 100 - 2 × (3³) + √144 - 72/8
  3. 25 + 8 × (5²) - √49 + 45/5

Solve them step-by-step, following the order of operations, and see if you can get the correct answers. Don't be afraid to make mistakes – that's how we learn! And if you get stuck, just refer back to the steps we outlined in this guide.

Keep up the great work, guys! You've got this! Math is all about understanding the rules and applying them consistently. With a little practice and a positive attitude, you can conquer any mathematical challenge that comes your way. Remember, each problem you solve makes you a stronger and more confident mathematician. Happy solving!