Math Problem: Step-by-Step Solution & Explanation

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Hey math enthusiasts! Let's break down the math problem: (3/2) * (1.2 + 3/5) - √1.21. No worries, we'll go through it step by step, so even if math isn't your favorite subject, you'll totally get it by the end. This is a classic example of how to apply the order of operations, and we'll cover each part in detail. Get ready to flex those math muscles!

Understanding the Order of Operations

Before we dive in, let's quickly recap the order of operations. You might know it as PEMDAS or BODMAS. Basically, it's the rulebook for solving math problems in the correct order. Here's a quick reminder:

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

Following this order ensures everyone gets the same answer. It's like a secret code to solve any math equation, no matter how complex it seems. In our case, we'll follow these steps to simplify the expression and arrive at the final solution. The first thing you need to remember is to handle what's inside the parentheses. This will make the rest of the problem way easier to solve, so let's start there. The order of operations is crucial for getting the correct answer, and it helps to break down complex problems into smaller, more manageable steps. It's like a recipe; you follow the instructions in order to get the desired result. Without this order, you could get a totally different (and wrong) answer! Also, remember to handle exponents and roots before doing multiplication and division. The reason for this order is to ensure mathematical consistency. Imagine if everyone solved the same problem differently; it would be utter chaos! The order of operations brings structure and clarity to math, making it a universal language.

Simplifying Parentheses and Brackets

Alright, let's start with the parentheses: (1.2 + 3/5). First off, let's get that fraction, 3/5, into a decimal. Guys, remember that 3 divided by 5 is 0.6. So, the expression inside the parentheses becomes (1.2 + 0.6). Now, that's easy-peasy! Adding 1.2 and 0.6 gives us 1.8. So, the simplified expression inside the parentheses is 1.8. We're getting closer to solving this problem, and by simplifying the parentheses first, it makes the rest of the calculation way more straightforward. Also, handling the fractions early on reduces the chances of errors and keeps the process smooth.

Before we move on, let's recap. Inside the parentheses, we had to change the fraction into a decimal to make the addition easier. It's all about making the steps as simple as possible. Breaking it down this way ensures we don't make any silly mistakes along the way. Converting fractions to decimals or decimals to fractions is a skill that can be useful in all kinds of math problems. The point is to make the problem easier for yourself, and there's no single way to approach a problem; choose the method that works best for you. Now, let's move on to the next step and continue simplifying the expression.

Solving the Multiplication Part

Now that we've taken care of the parentheses, our expression looks like this: (3/2) * 1.8 - √1.21. Next up, multiplication! We need to multiply 3/2 by 1.8. First things first, let's turn 3/2 into a decimal. Three divided by two is 1.5. So, we're doing 1.5 * 1.8. Multiplying 1.5 by 1.8 gives us 2.7. So, the multiplication part simplifies to 2.7. See? Not too hard, right?

Converting Fractions and Decimals

Quick tip: When you're dealing with fractions and decimals in the same problem, it often helps to convert everything to decimals. It makes the calculations easier and reduces the chance of making a mistake. Also, don't be afraid to use a calculator for these steps! Math is not always about doing everything in your head; it's about understanding the concepts and knowing how to apply them. The goal is always to get the correct answer efficiently. Therefore, a calculator is a great tool for quickly checking your work and focusing on the problem-solving strategy. Always remember to double-check your calculations, especially when dealing with multiple steps.

Dealing with the Square Root

We're almost there, folks! Now, let's handle the square root: √1.21. The square root of 1.21 is 1.1. So, we've simplified that part. Now, our expression is 2.7 - 1.1. Remember, the square root of a number is a value that, when multiplied by itself, equals the original number. Learning how to identify and calculate square roots is an essential math skill. And, again, there's no shame in using a calculator to find the square root; it's all about getting to the correct answer. The more you practice, the easier it gets. It is a good idea to remember some of the most common square roots, like the square root of 4, 9, 16, and 25. Understanding how to work with square roots is important in many areas of math and science, so this step is super crucial.

Square Root Calculation Explained

When calculating square roots, it's also helpful to recognize perfect squares. These are numbers that result from squaring a whole number (like 1, 4, 9, 16, 25, etc.). Knowing these perfect squares can help you quickly identify the square root. Also, remember that a square root can be either positive or negative. However, in most basic problems, we consider only the positive square root. You might encounter negative square roots in more advanced math, but for now, stick with the basics. Practice makes perfect, and the more you work with square roots, the more comfortable you'll become. So, keep at it!

Final Calculation: Subtraction

Okay, we're on the home stretch! Our expression is now 2.7 - 1.1. Subtracting 1.1 from 2.7 gives us 1.6. And there you have it, folks! The answer to the math problem (3/2) * (1.2 + 3/5) - √1.21 is 1.6. High five!

Double-Checking Your Work

It's always a good idea to double-check your answer. You can do this by going back through each step and making sure you didn't miss anything. If you're feeling extra cautious, use a calculator to work through the entire problem again. This is a good way to verify that you didn't make any errors. Also, don't be afraid to ask for help! Math can be tricky, and there's no shame in getting a second opinion or asking a friend or teacher to review your work.

Summary of the Steps

Let's quickly recap what we did:

  1. Solved the parentheses: (1.2 + 3/5) = 1.8
  2. Multiplied: (3/2) * 1.8 = 2.7
  3. Calculated the square root: √1.21 = 1.1
  4. Subtracted: 2.7 - 1.1 = 1.6

Conclusion

So, there you have it! We've successfully solved the math problem step by step. Remember the order of operations, and don't be afraid to break down the problem into smaller pieces. You've got this! Keep practicing, and you'll become a math whiz in no time. Learning math is a journey, not a race. Each problem you solve builds your confidence and skills. So, embrace the challenge, enjoy the process, and celebrate your successes. Also, don't forget that math is all around us, from calculating the best deals at the grocery store to figuring out how far you can drive on a tank of gas. Math helps us make sense of the world, so keep exploring and have fun with it!