Math Problem: Finding A Number From A Percentage Calculation

by ADMIN 61 views

Hey guys! Ever get those math problems that look like they're speaking another language? We've got one of those today, but don't worry, we're going to break it down step by step and make it super easy to understand. Our main goal here is to find a mystery number. We know that a specific percentage of this number equals a rather complex mathematical expression. Let's dive in and figure it out together!

Understanding the Question

Our mission, should we choose to accept it (and we do!), is to find a number. The clue we have is this: 33 1/3% of this secret number is the same as the result of a calculation: ((9 1/5 - 3.68) / 2 1/2) * (1 / (2.1 - 2.09)). See? It looks intimidating, but it's just a bunch of smaller calculations hiding inside a bigger one. To solve this effectively, we will meticulously dissect each component of the equation. This involves converting mixed numbers to decimals, performing the arithmetic operations in the correct order (PEMDAS/BODMAS, anyone?), and finally, using the percentage information to reverse-engineer our mystery number. It’s like being a mathematical detective, piecing together clues to crack the case!

First, let’s convert 33 1/3% into a fraction. Remember that percentages are just fractions out of 100. So, 33 1/3% is the same as 33.333...%, which we all know and love as 1/3. This conversion is crucial because it simplifies the equation significantly. Using fractions often makes calculations cleaner and less prone to rounding errors compared to decimals. Next, we focus on the right side of the equation, that behemoth of numbers and parentheses. We will tackle it piece by piece, starting from the innermost operations and working our way outwards. This methodical approach ensures we don't miss any steps and maintain accuracy throughout the process. Think of it as building a puzzle – you start with the easy bits and gradually connect them to form the complete picture.

Solving the Expression

Okay, let's untangle this mathematical beast! We’ll start with the expression: ((9 1/5 - 3.68) / 2 1/2) * (1 / (2.1 - 2.09)). Remember PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)? That’s our guide here.

Step 1: Parentheses Power!

We've got nested parentheses, so we start with the innermost ones.

  • (9 1/5 - 3.68): First, let's convert 9 1/5 to a decimal. 1/5 is 0.2, so 9 1/5 is 9.2. Now we have 9.2 - 3.68 = 5.52. Make sure you line up those decimals!
  • (2.1 - 2.09): This one’s a bit easier. 2.1 - 2.09 = 0.01. Simple subtraction, but crucial for accuracy. Now our expression looks like this: ((5.52) / 2 1/2) * (1 / (0.01))

Step 2: Still in Parentheses!

We’ve still got those bigger parentheses to deal with.

  • (5.52) / 2 1/2: Let's convert 2 1/2 to a decimal, which is 2.5. Now we have 5.52 / 2.5 = 2.208. Time for some long division, or a calculator if you prefer! Now we have (2.208) * (1 / (0.01))
  • (1 / (0.01)): This is the same as 1 divided by 0.01, which equals 100. Dividing by a small decimal can be tricky, so double-check your work! Our expression is now super streamlined: 2.208 * 100

Step 3: Multiplication Time!

Finally, we multiply: 2.208 * 100 = 220.8. Multiplying by 100 is just moving the decimal point two places to the right.

Phew! We made it through the calculation jungle. The right side of our equation is equal to 220.8. Remember, this is the value of 1/3 of our mystery number. We're in the home stretch now!

Finding the Mystery Number

Alright, we know that 1/3 of our mystery number is 220.8. To find the whole number, we need to reverse the operation. If we divided by 3 to get 220.8, we need to multiply by 3 to get back to the original number. This is a fundamental concept in algebra: using inverse operations to solve for unknowns. Think of it like this: if you know a slice of a pie represents 1/3 of the whole pie, you need three slices to make the entire pie. The same logic applies to numbers!

So, let’s do the math: 220.8 * 3 = 662.4. Grab your calculator, or brush up on your multiplication skills! And there we have it! Our mystery number is 662.4. Isn't it satisfying when a complex problem unravels into a clear solution? It’s like cracking a code, and the feeling of accomplishment is totally worth the effort.

Conclusion

We did it! We successfully navigated the mathematical maze and found the number. The key was to break the problem down into smaller, manageable steps and tackle each one methodically. Remember, math problems can seem daunting at first, but with a little patience and a step-by-step approach, you can conquer anything! Always double-check your work, and don’t be afraid to ask for help when you need it. Math is a team sport sometimes! And most importantly, celebrate your victories, big or small. Every problem solved is a step forward in your mathematical journey. Keep practicing, keep learning, and keep those numbers crunching!

So, to recap, we started with a complex expression involving percentages, mixed numbers, and nested parentheses. We meticulously simplified each component, applying the order of operations (PEMDAS/BODMAS) to maintain accuracy. We converted percentages to fractions, handled decimal operations, and finally, used inverse operations to solve for the unknown number. The journey may have been challenging, but the result – the satisfying discovery of 662.4 – makes it all worthwhile. Now you've got another tool in your math toolkit! Go forth and conquer more mathematical challenges!