Solve 120 ÷ 250 - [120 + (81 - 39)] Step-by-Step

by Marta Kowalska 49 views

Hey guys! Ever get that sinking feeling when you see a complex mathematical expression staring back at you? Don't worry, we've all been there! Math can seem intimidating, but trust me, breaking it down into manageable steps makes it so much easier. In this guide, we're going to tackle a specific expression: 120 ÷ 250 - [120 + (81 - 39)]. We'll go through each step nice and slow, so you can follow along and conquer these types of problems with confidence. Let's dive in!

Understanding the Order of Operations (PEMDAS/BODMAS)

Before we even think about plugging in numbers, we need to understand the golden rule of mathematical expressions: the order of operations. You might have heard of it as PEMDAS or BODMAS. It's basically a set of rules that tells us the order in which we need to perform calculations to get the right answer. Think of it as the recipe for solving math problems!

PEMDAS stands for:

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

BODMAS is essentially the same thing, just with slightly different names:

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

See? Same order, just different words! The important thing is understanding the hierarchy. Anything inside parentheses (or brackets) comes first. Then we deal with exponents (or orders). Multiplication and division are next, but we work them from left to right. Finally, we handle addition and subtraction, again from left to right. This left-to-right rule is crucial when you have both multiplication and division, or both addition and subtraction, in the same expression. Messing up the order of operations is like skipping a step in your favorite recipe – you probably won't end up with the delicious result you were hoping for!

Why is this order so important? Well, imagine you ignored it and just solved the problem from left to right. You'd likely get a completely different answer, and that answer wouldn't be mathematically correct. The order of operations ensures we all follow the same rules, so we arrive at the same, accurate solution. It’s the universal language of math, making sure everyone’s on the same page. So, let's keep PEMDAS/BODMAS in the back of our minds as we tackle our expression: 120 ÷ 250 - [120 + (81 - 39)]. This is our guiding star in this mathematical adventure, ensuring we don’t get lost in the numbers!

Breaking Down the Expression: 120 ÷ 250 - [120 + (81 - 39)]

Okay, let's bring back our mathematical challenge: 120 ÷ 250 - [120 + (81 - 39)]. It looks a bit scary at first glance, right? But don't fret! We're going to break it down piece by piece, just like a detective solving a case. Remember, our trusty friend PEMDAS (or BODMAS) is here to guide us. The first thing we spot is those parentheses, and as PEMDAS dictates, they're our first target. Inside the parentheses, we have (81 - 39). This is a straightforward subtraction, and we can handle it without any drama. So, 81 minus 39 equals 42. Great! We've conquered the parentheses.

Now our expression looks a little less intimidating: 120 ÷ 250 - [120 + 42]. See? We're making progress! Next up, we have those square brackets. Remember, brackets are just another form of parentheses, so we treat them the same way. Inside the brackets, we have 120 + 42. This is another simple addition problem. Adding 120 and 42 gives us 162. Fantastic! We've cleared the brackets, and the expression is shrinking down.

Our expression is now looking much more manageable: 120 ÷ 250 - 162. We're getting there! Now, according to PEMDAS, we need to look for any exponents (or orders). But guess what? There aren't any in this expression, so we can skip that step. Next up is multiplication and division. Ah, there's a division! We have 120 ÷ 250. This is where things might get a little tricky, as it doesn't divide perfectly. We can express this as a fraction (120/250) or perform the division to get a decimal. For now, let's perform the division. 120 divided by 250 equals 0.48. We’ve tackled the division, and our expression is becoming simpler and simpler.

Now we're left with 0.48 - 162. This is the final stretch! We have a subtraction problem. Subtracting 162 from 0.48 gives us a negative number: -161.52. And there we have it! We've successfully navigated the entire expression, step by step, following the sacred order of operations. The solution to 120 ÷ 250 - [120 + (81 - 39)] is -161.52. See, it wasn't so scary after all, right? Just remember to break it down, follow PEMDAS, and you'll be a math-solving pro in no time!

Step-by-Step Solution Walkthrough

Let's solidify our understanding by walking through the entire solution one more time, step-by-step. This will help you internalize the process and feel even more confident when you encounter similar problems in the future. We'll lay it all out nice and clear, so there's no room for confusion.

Step 1: Parentheses (Innermost First)

Our original expression is: 120 ÷ 250 - [120 + (81 - 39)]. The first thing we need to address is the innermost parentheses: (81 - 39). 81 - 39 = 42. So, we replace (81 - 39) with 42. Our expression now looks like this: 120 ÷ 250 - [120 + 42].

Step 2: Brackets (Outer Parentheses)

Next, we tackle the brackets: [120 + 42]. Remember, brackets are just another form of parentheses, so we treat them the same. 120 + 42 = 162. We replace [120 + 42] with 162. Our expression is now simplified to: 120 ÷ 250 - 162.

Step 3: Division

According to PEMDAS, we handle division before subtraction. So, we need to calculate 120 ÷ 250. 120 ÷ 250 = 0.48. We replace 120 ÷ 250 with 0.48. Our expression is now: 0.48 - 162.

Step 4: Subtraction

Finally, we perform the subtraction: 0.48 - 162. 0.48 - 162 = -161.52.

Therefore, the final answer is -161.52.

See how we methodically worked through the expression? Each step was clear and logical, thanks to our friend PEMDAS. By breaking down the problem into smaller, manageable chunks, we were able to conquer it with ease. This step-by-step approach is the key to solving complex mathematical expressions. Practice makes perfect, so the more you work through these types of problems, the more natural the process will become. You'll be a math whiz in no time!

Common Mistakes to Avoid

Alright, now that we've mastered solving this expression, let's talk about some common pitfalls that people often stumble into. Knowing these mistakes beforehand can save you a lot of headaches and ensure you get the correct answer. It's like knowing the traps in a video game – you can avoid them and level up your math skills!

The biggest mistake, hands down, is messing up the order of operations. We can't stress this enough! PEMDAS/BODMAS is your best friend. If you skip a step or perform operations in the wrong order, you're almost guaranteed to get the wrong result. For example, if you subtracted 162 from 250 before doing the division in our problem, you'd be way off. Always double-check that you're following the correct sequence.

Another common error is mishandling negative signs. These little guys can be sneaky! Remember that a negative sign in front of a number applies to that entire number. When you're performing operations with negative numbers, it's super important to pay close attention to the rules of addition, subtraction, multiplication, and division with negatives. For instance, subtracting a negative number is the same as adding a positive number. Keep those rules in mind!

Forgetting to distribute is another trap. If you have a number multiplying an expression inside parentheses, you need to distribute that number to every term inside the parentheses. It's like making sure everyone gets a piece of the pie. If you forget to distribute, you'll only be working with part of the expression, and your answer will be incomplete.

Finally, a simple but surprisingly common mistake is arithmetic errors. We're all human, and sometimes we make silly calculation mistakes. It's easy to add or subtract incorrectly, especially when you're dealing with larger numbers or working quickly. The best way to avoid these errors is to double-check your work. Take your time, write neatly, and if possible, use a calculator to verify your calculations. A little extra care can go a long way!

By being aware of these common mistakes, you can actively avoid them. Remember, math is like a puzzle – each piece needs to fit perfectly. By paying attention to the details, following the rules, and double-checking your work, you'll be solving mathematical expressions like a pro!

Practice Makes Perfect: Similar Expressions to Try

Okay, guys, we've covered a lot! We've dissected our expression, walked through the solution step-by-step, and even learned about common mistakes to avoid. But the real key to mastering math is practice, practice, practice! So, let's put your newfound skills to the test. Here are a few similar expressions for you to try on your own. Don't worry, you've got this!

  1. 200 + 50 ÷ 2 - (15 x 3)
  2. 150 - [75 + (20 ÷ 4)] x 2
  3. (10 + 5) ² - 100 ÷ 5

Remember to use PEMDAS/BODMAS as your guide, and break each expression down into manageable steps. Don't be afraid to write out each step clearly, just like we did in our walkthrough. This will help you stay organized and avoid those pesky mistakes. And if you get stuck, don't hesitate to review the steps we covered earlier in this guide.

For the first expression, focus on handling the parentheses and multiplication/division before tackling addition and subtraction. In the second expression, pay close attention to the brackets and the order of operations within them. And for the third expression, remember that the exponent comes before division. These little nuances are what make math challenging, but also incredibly rewarding when you crack the code!

The most important thing is to not get discouraged. Math is a skill that improves with practice. The more you challenge yourself with problems like these, the more confident and proficient you'll become. So, grab a pencil and paper, and give these expressions a try. You might surprise yourself with how much you've learned! And who knows, you might even start to enjoy the process of solving mathematical puzzles. Happy calculating!