Simplifying Math Problems: A Step-by-Step Guide

by SLV Team 48 views
Simplifying Math Problems: A Step-by-Step Guide

Hey guys! Let's dive into some math problems and learn how to simplify them. Simplifying mathematical expressions is a fundamental skill in mathematics, and it's super important for solving more complex problems. It makes the problems easier to understand and work with. So, buckle up, and let's break down these expressions step by step. We'll go through each problem, explaining the process and the logic behind it, so you can ace your math homework or any other math-related challenges. We'll cover everything from basic arithmetic operations to dealing with fractions and square roots. By the end, you'll be able to simplify a wide range of mathematical expressions with confidence. Are you ready?

Problem 1: 54 - 24 - 16

Alright, let's start with the first problem: 54 - 24 - 16. This one's pretty straightforward, involving only subtraction. The key here is to perform the operations from left to right. First, we subtract 24 from 54. So, 54 minus 24 equals 30. Then, we take that result (30) and subtract 16 from it. 30 minus 16 equals 14. Therefore, the simplified answer for this expression is 14. Remember, when you have multiple subtraction operations, always work from left to right. This ensures that you don't mess up the order of operations, which can lead to incorrect answers. It's really that simple! Always double-check your calculations, especially when you're just starting out. Make sure you're subtracting correctly. You can even use a calculator to verify your answers, but make sure you understand the process first. This way, you'll not only get the correct answers but also build a solid foundation in arithmetic. And trust me, the more you practice, the easier it gets!

To summarize, we followed these steps:

  1. 54 - 24 = 30
  2. 30 - 16 = 14

So, the final answer is 14. Easy peasy, right?

Problem 2: 40 + 1029 - 5625

Next up, we have 40 + 1029 - 5625. This problem includes addition and subtraction. Again, we'll follow the order of operations from left to right. First, we add 40 and 1029. 40 plus 1029 equals 1069. Then, we subtract 5625 from that result. 1069 minus 5625 equals -4556. Therefore, the simplified answer for this expression is -4556. Remember that the order of operations is crucial. When you have a combination of addition and subtraction, perform them from left to right. Pay close attention to the signs – positive and negative numbers. Make sure you're subtracting the larger number from the smaller one when necessary, and don't forget the negative sign in the answer. Sometimes, these problems might seem intimidating because of the size of the numbers, but the process remains the same. Break it down into smaller steps, and you'll always reach the correct solution. Taking it one step at a time makes the problem much more manageable. Use a calculator to double-check your work, especially when dealing with larger numbers, to avoid any silly mistakes. The most important thing is to understand the logic behind each step.

Here’s a breakdown:

  1. 40 + 1029 = 1069
  2. 1069 - 5625 = -4556

The final answer is -4556.

Problem 3: 2/250 - 4724 - 6716 + 72187

Let's get into the next one: 2/250 - 4724 - 6716 + 72187. This one includes division, subtraction, and addition. First, we need to handle the division part. So, 2 divided by 250 equals 0.008. Now, we proceed with the rest of the operations from left to right. We start with the subtraction. 0.008 minus 4724 equals -4723.992. Then, we subtract 6716 from that result. -4723.992 minus 6716 equals -11439.992. Finally, we add 72187 to the result. -11439.992 plus 72187 equals 60747.008. So, the simplified answer for this expression is 60747.008. This problem demonstrates that order of operations matters, even when dealing with decimals. Remember to perform division before addition and subtraction unless parentheses dictate otherwise. Double-check your calculations with a calculator to make sure you're getting the decimals correct. It's easy to make mistakes with decimals, so take your time and be careful. Practicing these types of problems will help you become more comfortable with a variety of mathematical operations. It's also a good idea to write down each step, so you can easily identify any errors. Always break the problem into smaller steps. This will make it easier to solve, and you’re less likely to make mistakes.

Let’s summarize the steps:

  1. 2 / 250 = 0.008
  2. 0.008 - 4724 = -4723.992
  3. -4723.992 - 6716 = -11439.992
  4. -11439.992 + 72187 = 60747.008

The final answer is 60747.008.

Problem 4: 57/48 - 383645 - 2/384 + 451715

Moving on to 57/48 - 383645 - 2/384 + 451715. We've got division, subtraction, and addition again. Let's start with the division. 57 divided by 48 is approximately 1.1875. Also, 2 divided by 384 is approximately 0.0052. Now we can rewrite the expression as 1.1875 - 383645 - 0.0052 + 451715. Let’s work from left to right. First, we have 1.1875 minus 383645, which results in -383643.8125. Next, subtract 0.0052 from that, giving us -383643.8177. Finally, we add 451715 to this result. -383643.8177 plus 451715 equals 68071.1823. Thus, the simplified answer for this expression is 68071.1823. Remember that it's important to be organized with these calculations. Writing down each step helps in avoiding mistakes and makes it easier to review your work. Using a calculator is a great way to handle the calculations, especially when you are dealing with decimals, but make sure you understand the order of operations. Also, pay attention to the signs and keep everything in the right order. Practicing similar problems frequently will build your confidence and make you more proficient at simplifying expressions.

Here’s a breakdown:

  1. 57 / 48 ≈ 1.1875
  2. 2 / 384 ≈ 0.0052
  3. 1.1875 - 383645 ≈ -383643.8125
  4. -383643.8125 - 0.0052 ≈ -383643.8177
  5. -383643.8177 + 451715 ≈ 68071.1823

The final answer is approximately 68071.1823.

Problem 5: 81 - 37375 + 7686 + 2√648

Let's get to 81 - 37375 + 7686 + 2√648. This one introduces a square root. First, we need to calculate the square root of 648. The square root of 648 is approximately 25.456. Now we can rewrite the expression. So, the original expression becomes 81 - 37375 + 7686 + 2 * 25.456. Next, multiply 2 by 25.456, which gives us 50.912. The expression now looks like this: 81 - 37375 + 7686 + 50.912. Finally, let’s go from left to right: 81 minus 37375 equals -37294. Then, add 7686 to that, resulting in -29608. Then add 50.912, which gives us -29557.088. So, the simplified answer for this expression is -29557.088. Dealing with square roots requires knowing that you first need to find the square root, and then proceed with the remaining operations in the order of operations. Be sure you know how to find the square root and remember the correct order of operations to avoid mistakes. Ensure you calculate the square root properly and then multiply it by the coefficient, in this case, 2. Be careful while typing numbers into your calculator, and always double-check your calculations to avoid small errors that can greatly change the final answer. Practicing different types of problems is very helpful in building problem-solving skills.

Here's how we did it:

  1. √648 ≈ 25.456
  2. 2 * 25.456 ≈ 50.912
  3. 81 - 37375 = -37294
  4. -37294 + 7686 = -29608
  5. -29608 + 50.912 ≈ -29557.088

The final answer is approximately -29557.088.

Problem 6: }/24 - 45 + 1375 -- + 128

Let’s move on to }/24 - 45 + 1375 -- + 128. I think there's a typo in the original expression, so let’s correct it. Based on the context, it should probably be something like: 8 / 24 - 45 + 1375 - 128. We need to begin by performing the division. 8 divided by 24 is approximately 0.333. Now we have 0.333 - 45 + 1375 - 128. Let’s proceed with our calculations, starting from the left. 0.333 minus 45 is -44.667. Next, we add 1375, which gives us 1330.333. Subtracting 128 from that yields 1202.333. The simplified answer to this expression is 1202.333. This problem shows us the importance of correctly interpreting the question and correcting any possible typos to get a correct solution. Reviewing the initial expression and identifying typos are crucial steps in solving any math problem. We must also follow the correct order of operations, and pay close attention to signs to make sure you get the right answer. Using a calculator to double-check each step is always a great practice to reduce errors. As you get more used to the process, you can solve these problems with confidence.

Here’s a breakdown:

  1. 8 / 24 ≈ 0.333
  2. 0.333 - 45 ≈ -44.667
  3. -44.667 + 1375 ≈ 1330.333
  4. 1330.333 - 128 ≈ 1202.333

The final answer is approximately 1202.333.

Problem 7: +625 -- 192 + √1715 - 1536

Lastly, let's look at +625 - 192 + √1715 - 1536. This one involves a square root. Let's start by calculating the square root of 1715, which is approximately 41.412. Rewrite the original expression as 625 - 192 + 41.412 - 1536. Now, follow the order of operations from left to right. 625 minus 192 equals 433. Adding 41.412 gives us 474.412. Then subtract 1536, and the result is -1061.588. Therefore, the simplified answer for this expression is -1061.588. Once again, remember that handling square roots requires us to compute the square root first before doing any other operation. We need to remember to pay close attention to the order of operations to make sure everything is calculated in the right order. Practicing different types of problems, including those involving square roots and multiple operations, will improve your ability to quickly and accurately simplify math expressions. Ensure you understand the basics before moving on to more complex math problems. It's also important to check your answers frequently, and using a calculator will help you with this.

Here’s how we did it:

  1. √1715 ≈ 41.412
  2. 625 - 192 = 433
  3. 433 + 41.412 ≈ 474.412
  4. 474.412 - 1536 ≈ -1061.588

The final answer is approximately -1061.588.

And that's it, guys! We have simplified all of the expressions. I hope this guide helps you understand how to simplify math problems. Remember to take it step by step, follow the order of operations, and practice regularly. Keep up the good work, and you'll become a math whiz in no time. Thanks for joining me, and see you in the next lesson!