Solve 113 + (25 - (-26) × (-8) ÷ 12) Easily

by Marta Kowalska 44 views

Hey guys! Today, we're going to break down a math problem that might look a bit intimidating at first glance: 113 + (25 - (-26) × (-8) ÷ 12). Don't worry, we'll tackle it step by step, making sure everyone understands each part of the process. We'll use the order of operations (PEMDAS/BODMAS) to guide us. So, grab your calculators (or your mental math skills!), and let's dive in!

Understanding PEMDAS/BODMAS

Before we jump into the problem, let's quickly review PEMDAS/BODMAS. This acronym helps us remember the correct order of operations in mathematics:

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

Keeping this order in mind is crucial for solving complex equations accurately. It ensures that we perform operations in the correct sequence, leading to the right answer. Think of it as the golden rule of math – follow it, and you'll succeed!

Step 1: Focusing on the Parentheses

Our problem has a set of parentheses: (25 - (-26) × (-8) ÷ 12). According to PEMDAS/BODMAS, we need to solve everything inside the parentheses first. This means we'll be dealing with multiplication, division, and subtraction within this section. Let's break it down further.

Step 1a: Multiplication

Inside the parentheses, we see (-26) × (-8). Remember that a negative number multiplied by another negative number results in a positive number. So, let's multiply: -26 * -8 = 208. Now our expression inside the parentheses looks like this: (25 - 208 ÷ 12). We've successfully handled the multiplication part!

Step 1b: Division

Next up, we have 208 ÷ 12. When we divide 208 by 12, we get approximately 17.33. So, let's plug that result back into our equation. Now the expression inside the parentheses is: (25 - 17.33). We're getting closer to simplifying the parentheses!

Step 1c: Subtraction

Now, let's subtract: 25 - 17.33 = 7.67. Great! We've simplified the entire expression within the parentheses down to a single number: 7.67. This was a significant step, and now our original problem looks much simpler: 113 + 7.67.

Step 2: Addition

We've cleared the parentheses, and now we're left with a simple addition problem: 113 + 7.67. Let's add these two numbers together. 113 + 7.67 = 120.67.

Final Answer

And there you have it! The solution to the problem 113 + (25 - (-26) × (-8) ÷ 12) is 120.67. We successfully navigated through the order of operations, simplified the expression step by step, and arrived at our final answer. Math problems might seem daunting at first, but by breaking them down into smaller, manageable steps, they become much easier to solve. Remember to always follow PEMDAS/BODMAS, and you'll be a math whiz in no time!

Common Mistakes to Avoid

When tackling problems like this, it's easy to make a few common mistakes. Let's highlight some pitfalls to avoid:

  • Ignoring the Order of Operations: This is the biggest mistake you can make. Always stick to PEMDAS/BODMAS. If you perform addition before multiplication, for example, you'll end up with the wrong answer.
  • Sign Errors: Keep a close eye on negative signs, especially when multiplying or dividing. A simple sign error can throw off your entire calculation.
  • Miscalculating Within Parentheses: Make sure you simplify everything inside the parentheses correctly before moving on. Double-check your work to avoid errors.
  • Rounding Too Early: If you round intermediate results (like in our division step), you might end up with a slightly inaccurate final answer. It's best to keep as many decimal places as possible until the very end.

By being mindful of these potential pitfalls, you can increase your accuracy and confidence when solving mathematical expressions.

Practice Problems

Want to sharpen your skills? Here are a few practice problems similar to the one we just solved:

  1. 50 + (15 - (-4) × 3 ÷ 2)
  2. 200 - (10 + 5 × (-6) ÷ 3)
  3. 75 + (30 - (-2) × (-7) ÷ 14)

Try solving these problems on your own, following the steps we discussed. Remember to break each problem down, work through the parentheses first, and adhere to PEMDAS/BODMAS. Practice makes perfect, and the more you work on these types of problems, the more comfortable you'll become with them.

Conclusion

So, guys, we've conquered a pretty interesting math problem today! We took 113 + (25 - (-26) × (-8) ÷ 12), and with a little PEMDAS/BODMAS magic, we got our answer: 120.67. The key takeaway here is that breaking down a complex problem into smaller, manageable steps makes everything less scary. Remember to always follow the order of operations, watch out for those tricky negative signs, and don't be afraid to double-check your work. Keep practicing, and before you know it, you'll be solving these problems in your sleep! Keep up the great work, and I'll see you in the next math adventure!