Calculate A + B: Step-by-Step Solution

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Calculate a + b: Step-by-Step Solution

Hey guys! Today, we're going to break down a math problem that might look a little intimidating at first, but trust me, it's totally manageable. We need to calculate the sum of a + b, where a = (1.2 : 0.5)² and b = (1.2 • 0.5)². We'll find the values of a and b separately and then add them together. So, grab your calculators (or your brainpower!) and let's get started!

Understanding the Problem

Before we dive into the calculations, let's make sure we understand what the problem is asking. We have two variables, a and b, each defined by an expression involving decimal numbers and exponents. The colon : represents division, and the bullet • represents multiplication. Our goal is to find the numerical values of a and b and then add those values together to get the final answer.

Breaking it Down:

  • We need to evaluate the expressions inside the parentheses first.
  • Then, we need to square the result (raise it to the power of 2).
  • Finally, we add the calculated values of a and b.

Calculating 'a'

The expression for a is (1.2 : 0.5)². Remember, the colon means division. So, we need to divide 1.2 by 0.5 first.

Step 1: Divide 1.2 by 0.5

1. 2 / 0.5 = 2.4

Think of it this way: how many halves (0.5) are there in 1.2? There are two whole halves in 1, and then another 0.4 is left, which is almost another half. So, two full halves and almost another one, totaling 2.4.

Step 2: Square the Result

Now that we know 1.2 / 0.5 = 2.4, we need to square this value. Squaring a number means multiplying it by itself.

2. 4² = 2.4 * 2.4

Let's do the multiplication:

2. 4 * 2.4 = 5.76

So, a = 5.76

Calculating 'b'

Now, let's calculate the value of b, which is (1.2 • 0.5)². The bullet • represents multiplication. So, we need to multiply 1.2 by 0.5 first.

Step 1: Multiply 1.2 by 0.5

3. 2 * 0.5 = 0.6

Multiplying by 0.5 is the same as finding half of the number. Half of 1.2 is 0.6.

Step 2: Square the Result

Now that we know 1.2 * 0.5 = 0.6, we need to square this value.

4. 6² = 0.6 * 0.6

Let's do the multiplication:

5. 6 * 0.6 = 0.36

So, b = 0.36

Finding the Sum: a + b

Now that we've calculated the values of a and b, we can add them together to find the final answer.

a = 5.76

b = 0.36

a + b = 5.76 + 0.36

Adding the Values:

6. 76 + 0.36 = 6.12

Therefore, the sum of a + b is 6.12

Analyzing the Answer Choices

The question provided multiple choice options:

A) 4

B) 5

C) 6

D) 7

Our calculated result of 6.12 does not directly match any of the provided options. Therefore, the question options are incorrect. The correct answer is 6.12

Conclusion

So, there you have it! By breaking down the problem into smaller, manageable steps, we were able to calculate the values of a and b and find their sum. Remember, the key to solving complex problems is to take it one step at a time. First, calculate the value inside the parentheses; second, calculate exponents, and last, add and subtract to get the final result. Keep practicing, and you'll become a math whiz in no time! Keep your mind sharp, and math will become easier.

Additional Tips for Solving Similar Problems

  • Pay Attention to Order of Operations: Always follow the order of operations (PEMDAS/BODMAS) to ensure you're performing calculations in the correct sequence.
  • Double-Check Your Work: It's easy to make a small mistake, so take a moment to review your calculations to catch any errors.
  • Use a Calculator: If you're allowed to use a calculator, take advantage of it to speed up the process and reduce the risk of errors.
  • Practice Regularly: The more you practice, the more comfortable you'll become with these types of problems.
  • Understand the Concepts: Don't just memorize formulas; make sure you understand the underlying concepts so you can apply them to different situations.
  • Estimate Your Answer: Before you start calculating, take a moment to estimate the answer. This can help you identify if your final answer is reasonable.

Common Mistakes to Avoid

  • Forgetting the Order of Operations: Not following PEMDAS/BODMAS can lead to incorrect results.
  • Incorrectly Squaring Numbers: Make sure you're multiplying the number by itself, not by 2.
  • Decimal Point Errors: Be careful when working with decimals to ensure you're placing the decimal point in the correct position.
  • Rushing Through the Problem: Take your time and work carefully to avoid making careless mistakes.
  • Not Checking Your Answer: Always double-check your work to catch any errors.

Remember: practice makes perfect! The more you work through problems like these, the easier they'll become. And don't be afraid to ask for help if you're struggling. There are plenty of resources available online and in your community to support you.

Real-World Applications

While this specific problem might seem abstract, the skills you're using to solve it are applicable in many real-world situations. For example:

  • Finance: Calculating interest rates, investment returns, and loan payments often involves exponents and decimal numbers.
  • Engineering: Engineers use mathematical calculations to design structures, machines, and systems.
  • Science: Scientists use mathematical models to describe and predict natural phenomena.
  • Everyday Life: Even simple tasks like calculating discounts, figuring out proportions in recipes, or estimating travel times involve mathematical skills.

By mastering these fundamental mathematical concepts, you're not just preparing for exams; you're also developing valuable skills that will serve you well in many aspects of life.

I hope this explanation was helpful and clear. If you have any questions, feel free to ask. Good luck with your studies, and keep up the great work! Remember that math is a tool and you should take advantage of it to solve all problems. Don't be discouraged if you find some challenges. We all find them. However, the most important is to keep going, and everything will be easier soon. You are capable of doing anything, always remember that!