Math Problems: Solutions And Explanations

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Hey everyone! Ready to dive into some math problems? We've got a few to work through, covering division, ratios, and proportions. Don't worry, I'll break down each problem step-by-step so you can totally understand how to solve them. Let's get started, shall we?

Problem 1: 0.13 / 26 = 18 / 49

Okay, this one might look a little tricky at first glance, but we can break it down! It seems like there might be a typo in the original problem. However, the intent is likely to solve equations with fractions. The best strategy here is to understand what the question is actually asking before solving the problem. Let's assume the original equation is asking to solve for x. We'll treat the original question as two separate equations, focusing first on the left side, then on the right side, making sure we are paying close attention to all numbers, decimals, and division signs.

  • First: We'll tackle 0.13 / 26. To solve this, we can think of it as 0.13 divided by 26. When you do the math, you get 0.005. So, 0.13 / 26 = 0.005.
  • Second: Now, let's look at 18 / 49. This is a simple division problem. When you calculate 18 divided by 49, you get approximately 0.367. So, 18 / 49 ≈ 0.367.

It seems like there's probably a typo in the initial prompt, the intention was to test your knowledge about solving for x in equations that may seem complicated, but by breaking them down into simple math problems, it all gets much easier. Remember, the key is always to solve what you understand first, and not to get overwhelmed by the symbols. The problem seems to be a typo, so let's move on to the next one!

Problem 2: x / 8 = 0.25 / 4

Alright, let's solve for x! This is a proportion problem, which means we're looking at two ratios that are equal to each other. To solve for x, we need to isolate it. Here's how we can do it:

  • Cross-Multiply: Multiply the numerator of the first fraction (x) by the denominator of the second fraction (4), and the denominator of the first fraction (8) by the numerator of the second fraction (0.25). This gives us 4x = 8 * 0.25.
  • Simplify: 8 * 0.25 equals 2. So, our equation becomes 4x = 2.
  • Isolate x: To get x by itself, we need to divide both sides of the equation by 4. This gives us x = 2 / 4.
  • Solve for x: Finally, 2 / 4 simplifies to 0.5. Therefore, x = 0.5. So, in the proportion x / 8 = 0.25 / 4, the value of x is 0.5. We can plug this value back into the original equation to confirm, in this way we learn to evaluate solutions with numbers.

Problem 3: 25 / 1850

This one is a straightforward division problem. We simply need to divide 25 by 1850. When we do the math, we get approximately 0.0135. It's as simple as that! Understanding basic division skills is the key to success in more complex problems, in this way, remember to keep things simple and learn the basics first!

Problem 4: x * 3 * 3 / 1851

This problem seems like another typo, but it is an invitation to think outside the box and understand how to solve for x. We need to interpret the original equation and see how we can solve for x, remember, when solving math problems, always focus on simplifying the math and solving the base problem first. We can rearrange the equation as follows:

  • Simplify the equation: Combine the 3's into 9x/1851. Now you have 9x = 1851.
  • Isolate x: Divide both sides by 9. This gives us x = 1851 / 9
  • Solve for x: When you divide 1851 by 9, you get 205.66. So, x = 205.66.

Problem 5: 14.4 / 16 = 2 / x

Okay, this is another proportion problem. Let's find the value of x. To solve for x, we'll follow these steps:

  • Cross-Multiply: Multiply 14.4 by x, and multiply 16 by 2. This gives us 14.4x = 32.
  • Isolate x: Divide both sides of the equation by 14.4. This gives us x = 32 / 14.4.
  • Solve for x: When you divide 32 by 14.4, you get approximately 2.22. Therefore, x ≈ 2.22. So, in the proportion 14.4 / 16 = 2 / x, the value of x is approximately 2.22. Always remember to simplify the math problem first to isolate x.

Problem 6: 1 / 1852

This is a straightforward division problem. We simply need to divide 1 by 1852. When we do the math, we get approximately 0.00054. It is just as simple as the previous division. Remember to always take your time and not rush the process!

Problem 7: x / 10 = 7.5 / 1.5

Let's solve for x in this proportion! Here’s how:

  • Cross-Multiply: Multiply x by 1.5, and multiply 10 by 7.5. This gives us 1.5x = 75.
  • Isolate x: Divide both sides of the equation by 1.5. This gives us x = 75 / 1.5.
  • Solve for x: When you divide 75 by 1.5, you get 50. Therefore, x = 50. So, in the proportion x / 10 = 7.5 / 1.5, the value of x is 50. The key to these problems is to always isolate x first.

Problem 8: x = 18 / 8

This is a pretty simple division problem! To find the value of x, we just need to divide 18 by 8. So:

  • Divide: 18 divided by 8 equals 2.25. Therefore, x = 2.25.

Problem 9: 3 / 5 / 0.125 / 2 = x

This problem involves several division operations. To solve for x, we need to perform these divisions step by step. To do it correctly, always start with the left side and keep moving to the right to simplify the problem:

  • First Division: Start with 3 divided by 5, which equals 0.6.
  • Second Division: Next, divide 0.6 by 0.125. This gives us 4.8.
  • Third Division: Finally, divide 4.8 by 2, which gives us 2.4. Therefore, x = 2.4. This problem demonstrates how important it is to pay attention to order when solving math problems, remember that the order of operations is key to finding the solution!

That's it, guys! We've worked through some math problems together. Hopefully, these explanations helped clarify how to solve them. Keep practicing, and you'll become a math whiz in no time! If you have any questions, feel free to ask. Happy calculating!