Solving (9.5 - 3 × 1 1/2) - 0.5: A Step-by-Step Guide

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Hey guys! Ever stumbled upon a math problem that looks like a jumbled mess of numbers and symbols? Well, today we're going to break down one of those problems step by step. We're diving into the expression (9.5 - 3 × 1 1/2) - 0.5. Don't worry, it's not as scary as it looks! We'll tackle each part of this equation, making sure you understand the process along the way. So, grab your calculators (or your brainpower!) and let's get started!

Understanding the Order of Operations

Before we jump into solving, it's super important to remember the golden rule of math: the order of operations. You might have heard of it as PEMDAS or BODMAS. This acronym tells us the exact order in which we need to perform calculations to get the right answer. Let's break it down:

  • Parentheses (or Brackets): Anything inside parentheses or brackets comes first.
  • Exponents (or Orders): Next, we deal with exponents (like squares and cubes).
  • Multiplication and Division: These are done from left to right.
  • Addition and Subtraction: Finally, addition and subtraction are performed from left to right.

Keeping this order in mind is crucial for solving our expression correctly. If we don't follow PEMDAS/BODMAS, we might end up with a completely different answer. So, let's make sure we stick to the plan!

In our specific problem, (9.5 - 3 × 1 1/2) - 0.5, we'll first focus on what's inside the parentheses. Within the parentheses, we have subtraction and multiplication. According to the order of operations, multiplication comes before subtraction. This means we need to multiply 3 by 1 1/2 before we subtract the result from 9.5. This meticulous approach ensures we solve the problem accurately and efficiently. Remember, math is like building a house – you need a solid foundation (understanding the rules) before you can start adding the walls (solving the problem).

Step 1: Converting the Mixed Number

The first thing we need to do is tackle that mixed number: 1 1/2. Mixed numbers can be a little tricky to work with directly, so let's convert it into an improper fraction. An improper fraction is simply a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). This conversion will make the multiplication step much smoother.

To convert 1 1/2 to an improper fraction, we follow these steps:

  1. Multiply the whole number (1) by the denominator (2): 1 × 2 = 2
  2. Add the numerator (1) to the result: 2 + 1 = 3
  3. Keep the same denominator (2).

So, 1 1/2 is equal to 3/2. Now we can rewrite our expression as (9.5 - 3 × 3/2) - 0.5. See? We're already making progress! By converting the mixed number to an improper fraction, we've simplified the expression and made it easier to work with. This is a common trick in math that can save you a lot of headaches down the road. Remember, the goal is to make the problem as manageable as possible before diving into the calculations.

Step 2: Performing the Multiplication

Now that we've converted the mixed number, let's move on to the multiplication part within the parentheses: 3 × 3/2. To multiply a whole number by a fraction, it's helpful to think of the whole number as a fraction as well. We can rewrite 3 as 3/1. So, our multiplication becomes 3/1 × 3/2.

To multiply fractions, we simply multiply the numerators together and the denominators together:

  • Numerator: 3 × 3 = 9
  • Denominator: 1 × 2 = 2

Therefore, 3 × 3/2 = 9/2. Now, let's rewrite our expression again: (9.5 - 9/2) - 0.5. We're getting closer to the solution! By performing the multiplication, we've further simplified the expression. Remember, each step we take is a step closer to the final answer. Breaking down the problem into smaller, manageable chunks makes it less intimidating and easier to solve. Keep up the great work!

We can also convert the improper fraction 9/2 to a decimal to make the subtraction easier. To do this, we simply divide the numerator (9) by the denominator (2): 9 ÷ 2 = 4.5. So, 9/2 is equal to 4.5. Now our expression looks even simpler: (9.5 - 4.5) - 0.5. See how converting to decimals can sometimes make things easier? It's all about finding the method that works best for you!

Step 3: Subtraction Inside the Parentheses

Alright, we've tackled the mixed number and the multiplication. Now it's time to handle the subtraction inside the parentheses: 9.5 - 4.5. This is a straightforward subtraction problem.

Subtracting 4.5 from 9.5, we get:

  1. 5 - 4.5 = 5

So, the expression inside the parentheses simplifies to 5. Our expression now looks like this: 5 - 0.5. We're almost there! By completing the subtraction inside the parentheses, we've significantly simplified the problem. Remember, the key to solving complex expressions is to break them down into smaller, more manageable steps. And look how far we've come! We've successfully navigated through the mixed number, multiplication, and subtraction within the parentheses. Just one more step to go!

Step 4: Final Subtraction

We're on the home stretch! The last step is to perform the final subtraction: 5 - 0.5. This is another simple subtraction problem.

Subtracting 0.5 from 5, we get:

5 - 0.5 = 4.5

And that's it! We've solved the expression. The final answer is 4.5. Give yourself a pat on the back – you've earned it! By following the order of operations and breaking down the problem into manageable steps, we were able to successfully navigate through the complexities of the expression. Remember, math is all about practice and patience. The more you practice, the more comfortable you'll become with solving these types of problems. And don't be afraid to ask for help when you need it. We're all in this together!

Conclusion

So, guys, we've successfully solved the mathematical expression (9.5 - 3 × 1 1/2) - 0.5, and the answer is 4.5. We tackled this problem by breaking it down into smaller, more manageable steps, remembering the order of operations (PEMDAS/BODMAS), and converting mixed numbers to improper fractions. This step-by-step approach is a fantastic way to handle any complex math problem. Remember, the key is to stay organized, be patient, and don't be afraid to make mistakes – they're part of the learning process!

I hope this guide has been helpful and has made solving this type of expression a little less daunting. Keep practicing, and you'll become a math whiz in no time! Now go out there and conquer those equations! You got this! And remember, math can be fun (sometimes!). Until next time, happy calculating!