Solving 5/9 Of (17/20 - 0.65) Divided By 2/21 A Step-by-Step Guide

Hey everyone! Today, we're diving headfirst into a math problem that looks a bit like a puzzle. We're going to break down each step, making it super easy to follow. Our mission? To solve this equation: 5/9 of (17/20 - 0.65) : 2/21. Sounds intriguing, right? Let's get started!

Unpacking the Problem

So, let's kick things off by really understanding the math problem. We've got a mix of fractions, decimals, and operations – a classic math challenge! The key here is to remember the order of operations (PEMDAS/BODMAS): Parentheses/Brackets first, then Exponents/Orders, Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right). This is our roadmap for success. First, we need to simplify inside the parentheses, then handle the "of" (which means multiplication), and finally tackle the division. By breaking it down like this, the problem becomes way less intimidating and much more manageable. Think of it like building with LEGOs – each step is a brick that, when placed correctly, completes the whole structure. We're not just crunching numbers; we're building a solution!

Step 1: Tackling the Parentheses (17/20 - 0.65)

The initial hurdle in our mathematical journey is deciphering what lies within the parentheses: 17/20 - 0.65. It's a mix of fractions and decimals, which means we need to find a common language between them. The easiest route? Converting the decimal to a fraction. We know that 0.65 is the same as 65/100. Now we have a fraction party! But before we jump into subtraction, let’s simplify 65/100. Both numbers can be divided by 5, giving us 13/20. Awesome! Now our problem looks cleaner: 17/20 - 13/20. Subtracting fractions is a breeze when they have the same denominator. We simply subtract the numerators (the top numbers) and keep the denominator (the bottom number) the same. So, 17 - 13 equals 4. This gives us 4/20. But wait, we're not done yet! 4/20 can be simplified further. Both 4 and 20 can be divided by 4, which leaves us with 1/5. So, after our first dive into the parentheses, we've emerged with a neat and tidy 1/5. Feels good, right? We've conquered the first challenge and are one step closer to the final answer.

Step 2: Unraveling "5/9 of (1/5)"

Now that we've successfully navigated the parentheses, it's time to tackle the next part of our equation: 5/9 of (1/5). Remember, in math lingo, "of" is code for multiplication. So, what we're really looking at is 5/9 multiplied by 1/5. Multiplying fractions might sound daunting, but it's actually super straightforward. You simply multiply the numerators (the top numbers) together and then multiply the denominators (the bottom numbers) together. Easy peasy! So, 5 multiplied by 1 is 5, and 9 multiplied by 5 is 45. This gives us 5/45. But hold on a second, our work isn't quite done yet. We always want to express our fractions in their simplest form. Looking at 5/45, we can see that both the numerator and the denominator can be divided by 5. When we do that, we get 1/9. Voila! We've simplified 5/9 of 1/5 to a much more manageable 1/9. We're making great progress, guys! Each step we conquer brings us closer to cracking the code of this mathematical puzzle.

Step 3: Dividing by 2/21

Alright, mathletes, we're on the home stretch! We've simplified the first two parts of our equation, and now we're left with the final boss: dividing by 2/21. This might seem tricky, but I promise it's not as scary as it looks. Dividing fractions is actually a clever little trick. Instead of dividing, we flip the second fraction (the one we're dividing by) and then multiply. It's like a mathematical magic trick! So, dividing by 2/21 becomes multiplying by 21/2. Now our problem looks like this: 1/9 multiplied by 21/2. Remember how we multiply fractions? We multiply the numerators and then multiply the denominators. 1 multiplied by 21 is 21, and 9 multiplied by 2 is 18. This gives us 21/18. But, as always, we want to simplify our fraction to its simplest form. Both 21 and 18 can be divided by 3. When we do that, we get 7/6. Now, 7/6 is what we call an improper fraction because the numerator is larger than the denominator. While it's a perfectly valid answer, sometimes it's nicer to express it as a mixed number. To do this, we see how many times 6 goes into 7, which is once, with a remainder of 1. So, 7/6 is the same as 1 and 1/6. And there you have it! We've conquered the division and arrived at our final answer.

The Grand Finale: Putting It All Together

After carefully navigating through parentheses, multiplication, and division, we've reached the end of our mathematical quest. We started with a complex-looking problem: 5/9 of (17/20 - 0.65) : 2/21, and we've broken it down step by step, making it super digestible. First, we tackled the parentheses, converting the decimal to a fraction and simplifying to get 1/5. Then, we handled the "of," which meant multiplying 5/9 by 1/5, resulting in 1/9. Finally, we faced the division, turning it into a multiplication by flipping the second fraction and simplifying 21/18 to its simplest form, 7/6, or 1 and 1/6 as a mixed number. So, the final answer to our problem is 7/6 or 1 1/6. Woo-hoo! Give yourselves a pat on the back, guys. You've successfully solved a multi-step math problem. This journey proves that even the most intimidating equations can be conquered if we break them down into smaller, manageable steps. Remember, math isn't about magic; it's about method. And you've mastered the method today!

Why This Matters: Math in the Real World

Now, you might be thinking, "Okay, cool, we solved a math problem. But when am I ever going to use this in real life?" That's a valid question! The truth is, math isn't just about numbers on a page; it's a way of thinking and problem-solving that's applicable in countless situations. Understanding fractions, decimals, and the order of operations might not seem like a superpower, but it's incredibly useful. Think about cooking, for instance. Recipes often call for measurements in fractions – half a cup of flour, a quarter teaspoon of salt. If you can confidently work with fractions, you can easily adjust recipes, double them, or halve them without messing things up. Budgeting and finance are another big one. Calculating discounts, figuring out interest rates, or splitting bills with friends all involve mathematical thinking. Knowing how to work with percentages and fractions can save you money and prevent financial headaches. Even in fields like engineering, architecture, and computer science, these fundamental math skills are essential building blocks. Engineers need to calculate stress and strain on materials, architects need to design spaces with precise dimensions, and programmers need to write code that performs complex calculations. So, the math we've done today isn't just an abstract exercise; it's a valuable tool that can help you navigate the world more effectively. By mastering these skills, you're not just acing math tests; you're equipping yourself for success in many areas of life.

Practice Makes Perfect: Keep the Math Magic Alive

So, we've conquered this equation together, and hopefully, you're feeling like math superheroes! But remember, like any skill, math takes practice. The more you flex those mathematical muscles, the stronger they'll become. Don't let this be a one-time thing! Challenge yourself to find math in your everyday life. When you're shopping, calculate the sale price of an item. When you're planning a road trip, figure out how long it will take to get there. When you're baking cookies, double or triple the recipe. The more you apply these concepts, the more natural they'll become. There are also tons of fantastic resources available to help you practice. Websites like Khan Academy, Mathway, and Wolfram Alpha offer free lessons, practice problems, and step-by-step solutions. You can also find fun math games and puzzles online that make learning enjoyable. Don't be afraid to ask for help. If you're struggling with a concept, reach out to your teacher, a tutor, or a friend who's good at math. Talking through problems can often make them click. Remember, everyone learns at their own pace, and it's okay to make mistakes. Mistakes are actually valuable learning opportunities! The key is to keep practicing, keep asking questions, and keep exploring the wonderful world of math. You've got this, guys! Let's continue our math adventures together.