Solving The Math Problem: 125/41:([5/122-3/183]+(-27)61)

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Hey everyone! Today, we're going to dive into a math problem that might seem a little intimidating at first glance: 125/41:([5/122-3/183]+(-27)61). Don't worry, we'll break it down step by step, making it super easy to understand. This problem involves a mix of fractions, addition, subtraction, and multiplication, but with a clear approach, we can totally conquer it! Let's get started and see how we can solve this math problem.

Breaking Down the Math Problem: Order of Operations

First things first, remember the order of operations! This is like the rulebook for solving math problems. We're talking about PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Following this order ensures we get the correct answer every time. In our problem, we've got parentheses, fractions, multiplication, addition, and division. So, we'll work from the inside out, starting with the innermost parentheses. This will allow us to solve the problem in the right order. Let's be careful when we approach the calculation.

Let's simplify the expression step by step to make things easier and avoid any mistakes. This also makes sure that the reader understands the steps involved in the process.

Tackling the Innermost Parentheses

Let's look at the innermost part: [5/122 - 3/183]. The first thing we need to do here is subtract the fractions. Before we can subtract fractions, we need a common denominator. Finding the least common multiple (LCM) of 122 and 183 might seem tricky at first, but let's break it down. Prime factorization is key here. We can factorize 122 as 2 * 61, and 183 as 3 * 61. The LCM is the product of the highest powers of all prime factors present. So, the LCM of 122 and 183 is 2 * 3 * 61 = 366. Now, we rewrite our fractions with the common denominator:

  • 5/122 becomes (5 * 3) / (122 * 3) = 15/366
  • 3/183 becomes (3 * 2) / (183 * 2) = 6/366

Now we can subtract the fractions: 15/366 - 6/366 = 9/366. We can simplify this fraction by dividing both the numerator and the denominator by 3, which gives us 3/122. This is the simplified result of the expression inside the first parentheses. This is not a very difficult process and we can solve it by using some basic mathematics operations and concepts.

Dealing with Multiplication Inside the Parentheses

Next, we have (-27) * 61. This is straightforward multiplication. -27 multiplied by 61 equals -1647. Now we can use this result to solve the original problem, moving step by step.

Combining the Simplified Terms

Now, let's go back to our original expression: [3/122 + (-1647)]. Adding a negative number is the same as subtracting, so this becomes 3/122 - 1647. To solve this, we can rewrite 1647 as a fraction with a denominator of 122: 1647 * 122/122 = 200934/122. So, our expression becomes 3/122 - 200934/122 = -200931/122. This is the result of the second parentheses. Now, we are getting closer to the solution.

Final Division

Finally, we have 125/41 : (-200931/122). Dividing by a fraction is the same as multiplying by its reciprocal. So, we flip the second fraction and multiply: 125/41 * (122/-200931). Multiply the numerators and denominators: (125 * 122) / (41 * -200931) = 15250 / -8238171. Now we can simplify it. Let's try simplifying the fractions. However, we can see that there is no common divisor for both the numerator and the denominator. The final answer is -15250/8238171. This is the final solution to our math problem!

Tips for Similar Math Problems

  • Always follow PEMDAS/BODMAS: This is your best friend! It helps you solve problems in the correct order.
  • Break it down: Complex problems become easier when you solve them step by step.
  • Practice: The more you practice, the better you'll become at solving these types of problems.
  • Check your work: Double-check your calculations to avoid silly mistakes.

Conclusion: You Got This!

So, there you have it! We've solved the math problem 125/41:([5/122-3/183]+(-27)61) together. It might have looked complicated at first, but by breaking it down into smaller steps, applying the order of operations, and being careful with our calculations, we were able to arrive at the solution of -15250/8238171. Remember, math is all about practice and understanding. Keep practicing, and you'll become a pro in no time. Keep up the great work, everyone! And until next time, happy calculating!

A Detailed Explanation

Let's get into a more detailed explanation to solidify our understanding. We'll revisit each step to make sure we've got everything covered, making sure everyone understands everything thoroughly. First, we have the main expression, which is a division problem: 125/41:([5/122-3/183]+(-27)61). We know we need to follow the order of operations. So, let's start inside the parentheses. Inside the parentheses, we have [5/122 - 3/183] + (-27 * 61). Notice that we have two distinct operations here: subtraction of fractions and multiplication.

Subtracting Fractions and Multiplication

Focusing on the fractions, we've got 5/122 - 3/183. To subtract these, we need a common denominator. Remember that we can find the common denominator by calculating the least common multiple (LCM) of the denominators (122 and 183). We can easily find the LCM as we did before, and we have to factorize these numbers. As we mentioned before, the LCM of 122 and 183 is 366. To rewrite our fractions with this common denominator, we do the following: (5/122) * (3/3) = 15/366 and (3/183) * (2/2) = 6/366. So, the subtraction becomes 15/366 - 6/366 = 9/366. This simplifies to 3/122. Now we have 3/122 as our result of subtracting the fractions. Now, let's handle the multiplication: (-27) * 61 = -1647. Combining these results, our expression within the parentheses becomes 3/122 - 1647. We need to simplify this result.

Combining the Results from the Parentheses

To subtract 1647 from 3/122, we need to convert 1647 into a fraction with a denominator of 122. We do this by multiplying 1647 by 122/122, which gives us 200934/122. Now, our expression within the parentheses is 3/122 - 200934/122. Subtracting these fractions gives us -200931/122. Thus, the entire expression within the parentheses simplifies to -200931/122. Therefore, this step is complete.

Final Division Operation

Our original problem was 125/41:([5/122-3/183]+(-27)61). Now that we've simplified the expression within the parentheses to -200931/122, our problem becomes 125/41 : (-200931/122). Remember that dividing by a fraction is the same as multiplying by the reciprocal of that fraction. So, we rewrite the division as multiplication and flip the second fraction: 125/41 * (122/-200931). Now, we multiply the numerators (125 * 122 = 15250) and the denominators (41 * -200931 = -8238171). This gives us 15250/-8238171. This is our final simplified result! This means the solution is -15250/8238171. We have successfully solved the initial problem. You can also divide these numbers, but the answer is a very long decimal number. We have found the final answer and explained how to solve it.

Step-by-Step Breakdown

Let's recap our steps to ensure we grasp the process thoroughly and make sure we haven't skipped any steps. Here's a detailed, step-by-step breakdown to make sure everything is crystal clear:

  1. Identify the problem: Our problem is 125/41 : ([5/122 - 3/183] + (-27 * 61)). We must remember that the order of operations is crucial here.
  2. Parentheses: We start with the parentheses. The expression inside is [5/122 - 3/183] + (-27 * 61).
  3. Inner Parentheses (Fractions): Within the parentheses, we have fractions. We find the LCM of 122 and 183, which is 366. We convert the fractions to have the common denominator: 5/122 becomes 15/366 and 3/183 becomes 6/366. Subtracting them, we get 15/366 - 6/366 = 9/366, which simplifies to 3/122.
  4. Inner Parentheses (Multiplication): We multiply: -27 * 61 = -1647.
  5. Combining Results: Combining the results from the fractions and multiplication, we have 3/122 - 1647. We convert 1647 into a fraction with a denominator of 122, giving us 200934/122. So, we have 3/122 - 200934/122 = -200931/122.
  6. Final Division: Back to the original problem, we had 125/41 : (-200931/122). Dividing by a fraction is the same as multiplying by its reciprocal. So, we have 125/41 * (122/-200931). Multiply the numerators (125 * 122 = 15250) and the denominators (41 * -200931 = -8238171), which gives us 15250/-8238171 or -15250/8238171.
  7. Solution: The solution to the original problem 125/41:([5/122-3/183]+(-27)61) is -15250/8238171.

This step-by-step approach ensures clarity and makes it easy to follow the entire process, which is very important. We have solved this problem in a systematic way and, in doing so, we learned how to approach similar problems in the future.