Order Of Operations: Calculate 150 + 150 - 150 * [192 - (152 + 53)]

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Order of Operations: Calculate 150 + 150 - 150 * [192 - (152 + 53)]

Hey guys! Let's break down this math problem step by step. We've got a bit of a beast here: 150 + 150 - 150 * [192 - (152 + 53)]. Don't worry, it's not as scary as it looks. We just need to remember our order of operations, often remembered by the acronym PEMDAS (or BODMAS):

  • Parentheses (or Brackets)
  • Exponents (or Orders)
  • Multiplication and Division
  • Addition and Subtraction

Following this order is crucial to getting the right answer. So, let's dive in!

Step-by-Step Calculation

1. Innermost Parentheses: (152 + 53)

First, we tackle the innermost parentheses: (152 + 53). This is a straightforward addition problem.

152 + 53 = 205

So, we can replace (152 + 53) with 205 in our original expression. The expression now looks like this:

150 + 150 - 150 * [192 - 205]

2. Outer Parentheses: [192 - 205]

Next up are the brackets, which are just another form of parentheses. We need to calculate [192 - 205]. This is a subtraction, but notice that we're subtracting a larger number from a smaller number, which will result in a negative value.

192 - 205 = -13

Now we substitute [192 - 205] with -13. Our expression is getting simpler:

150 + 150 - 150 * (-13)

3. Multiplication: 150 * (-13)

Now comes the multiplication part. We need to calculate 150 * (-13). Remember, multiplying a positive number by a negative number gives a negative result.

150 * (-13) = -1950

Replacing the multiplication part, our expression now looks like this:

150 + 150 - (-1950)

4. Subtraction of a Negative Number: - (-1950)

Here's a little trick to remember: subtracting a negative number is the same as adding a positive number. So, - (-1950) becomes + 1950. Our expression transforms into:

150 + 150 + 1950

5. Addition: 150 + 150 + 1950

Finally, we perform the additions from left to right.

First, add 150 and 150:

150 + 150 = 300

Now, add the result to 1950:

300 + 1950 = 2250

Final Answer

So, after carefully following the order of operations, we've found that:

150 + 150 - 150 * [192 - (152 + 53)] = 2250

The final answer is 2250.

Why Order of Operations Matters

You might be wondering, why all this fuss about the order? Well, if we didn't follow the correct order, we'd get a completely different answer. Imagine if we just went from left to right without considering parentheses or multiplication. We'd end up with a very wrong result!

For example, if we did the addition first, 150 + 150 = 300, then subtracted 150, we'd get 150. Then, if we tackled the rest haphazardly, we'd be miles away from the correct answer. That's why PEMDAS/BODMAS is our best friend in math!

Common Mistakes to Avoid

Here are a few common pitfalls to watch out for when tackling problems with order of operations:

  • Forgetting Parentheses: Always start with what's inside the parentheses or brackets. It's the golden rule!
  • Ignoring Multiplication/Division Precedence: Multiplication and division come before addition and subtraction. Don't just go from left to right.
  • Misunderstanding Negative Numbers: Remember the rules for multiplying and subtracting negative numbers. A negative times a negative is a positive, and subtracting a negative is the same as adding a positive.
  • Rushing: Take your time and break the problem down into smaller steps. It's easier to avoid mistakes when you're not rushing.

Real-World Applications

Order of operations isn't just some abstract math concept. It actually pops up in many real-world situations, especially in programming and finance.

  • Programming: When writing code, the order in which operations are performed is critical. A small mistake in the order can lead to a bug or incorrect output. Compilers and interpreters rely heavily on the order of operations to correctly evaluate expressions.
  • Finance: Calculating compound interest, figuring out loan payments, or analyzing investment returns all involve multiple operations that need to be performed in the correct order. Getting the order wrong could mean a significant error in your financial calculations.
  • Everyday Life: Even in everyday tasks like calculating the total cost of items with discounts and taxes, or figuring out cooking times for a recipe, we implicitly use the order of operations.

Practice Makes Perfect

The best way to master the order of operations is to practice! Try solving similar problems with different numbers and operations. You can find plenty of practice problems online or in math textbooks. The more you practice, the more comfortable you'll become with the rules and the faster you'll be able to solve these kinds of problems.

Tips and Tricks

  • Write it Out: Break down the problem into smaller steps and write each step down. This helps you stay organized and avoid mistakes.
  • Double-Check: After each step, double-check your calculations to make sure you haven't made any errors.
  • Use Mnemonics: Remember PEMDAS or BODMAS to keep the order of operations in mind.
  • Online Calculators: If you're stuck, you can use an online calculator or a scientific calculator to check your work, but always try to solve the problem yourself first.

Conclusion

So, there you have it! We've successfully calculated 150 + 150 - 150 * [192 - (152 + 53)] by following the order of operations. Remember, PEMDAS/BODMAS is your guide. Practice makes perfect, so keep at it, and you'll be a math whiz in no time! Keep an eye out for more math tips and tricks, and don't forget to share this with your friends if you found it helpful. Happy calculating, guys!