Solving 5/17 * 3 + 6 1/2: A Step-by-Step Guide

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Solving the Math Problem: 5/17 * 3 + 6 1/2

Hey guys! Today, we're diving into a math problem that might seem a little tricky at first glance, but don't worry, we'll break it down step-by-step. The problem is: 5/17 * 3 + 6 1/2. Math can be like a puzzle, and once you understand the rules, it becomes much easier to solve. We’ll tackle this by first understanding the order of operations, then converting mixed numbers, performing the multiplication, and finally, adding the fractions and whole numbers together. So, grab your pencils, and let’s get started! This is going to be fun, I promise!

Understanding the Order of Operations

Before we even touch the numbers, it’s super important to understand the order of operations. Think of it as the golden rule of math! We often use the acronym PEMDAS to remember it. PEMDAS stands for:

  • Parentheses: First, we solve anything inside parentheses.
  • Exponents: Next, we tackle exponents (like squares and cubes).
  • Multiplication and Division: These are done from left to right.
  • Addition and Subtraction: These are also done from left to right.

In our problem, 5/17 * 3 + 6 1/2, we have multiplication and addition. According to PEMDAS, we need to do the multiplication first before we add. This order ensures that everyone arrives at the same answer, no matter who's solving the problem. It's like following a recipe – if you mix the ingredients in the wrong order, you might not get the delicious cake you were hoping for!

Understanding this order is absolutely crucial for solving mathematical expressions correctly. Imagine if we added first and then multiplied – we'd end up with a completely different answer! So, keep PEMDAS in mind as we move forward. It's your trusty guide in the world of math. Remember, math is not just about getting the right answer; it's about understanding the process. And understanding the order of operations is the first big step in that process. Think of it as building a strong foundation for more complex math problems down the road. So, let’s keep this golden rule in our minds as we tackle the next steps!

Converting Mixed Numbers to Improper Fractions

Okay, now that we've got the order of operations down, let's look at our problem again: 5/17 * 3 + 6 1/2. Notice anything a little different? Yep, we have a mixed number: 6 1/2. A mixed number is just a combination of a whole number and a fraction. But to make our calculations easier, we need to convert this mixed number into an improper fraction. An improper fraction is simply a fraction where the numerator (the top number) is larger than or equal to the denominator (the bottom number).

So, how do we do this magic trick of converting 6 1/2 into an improper fraction? Here’s the simple formula:

  1. Multiply the whole number (6) by the denominator of the fraction (2).
  2. Add the result to the numerator of the fraction (1).
  3. Put this new number over the original denominator (2).

Let's do it together!

  • 6 * 2 = 12
  • 12 + 1 = 13
  • So, 6 1/2 becomes 13/2.

Isn’t that neat? Now we have a fraction that's much easier to work with in our equation. Converting mixed numbers to improper fractions might seem like an extra step, but it makes the rest of the calculations flow much more smoothly. It's like prepping your ingredients before you start cooking – it saves you time and stress in the long run! Remember, practice makes perfect, so the more you convert mixed numbers, the easier it will become. Soon, you'll be a pro at spotting them and turning them into improper fractions without even breaking a sweat. This skill is super useful not just for this problem, but for all sorts of math situations you'll encounter. So, let's keep building our math toolkit one step at a time!

Performing the Multiplication: 5/17 * 3

Alright, we've conquered the order of operations and the art of converting mixed numbers. Now, let's get to the heart of the problem: 5/17 * 3 + 13/2 (remember, we converted 6 1/2 to 13/2!). Following PEMDAS, we need to tackle the multiplication first. We're multiplying a fraction (5/17) by a whole number (3). How do we do that?

It's actually simpler than it looks! Just think of the whole number 3 as a fraction itself: 3/1. Any whole number can be written as a fraction by putting it over 1. Now our multiplication looks like this: 5/17 * 3/1.

To multiply fractions, we simply multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. So:

  • 5 * 3 = 15
  • 17 * 1 = 17

That means 5/17 * 3/1 = 15/17. See? Not so scary after all! We've successfully multiplied our fraction and whole number. This step is a crucial piece of the puzzle, and now we're one step closer to solving the whole problem. Multiplication of fractions might seem like a standalone skill, but it's a building block for so many other math concepts. Think about it – you use it in everything from calculating proportions to understanding percentages. So, mastering this skill is like adding a powerful tool to your math belt. And remember, every time you solve a problem like this, you're not just getting an answer; you're building confidence and competence in your math abilities. So, let's keep that momentum going and move on to the next step!

Adding the Fractions: 15/17 + 13/2

Fantastic! We've made great progress. We've simplified our problem to 15/17 + 13/2. Now comes the final act: adding these two fractions together. But, there's a little twist! We can only add fractions directly if they have the same denominator. Look at our fractions – we have 17 and 2 as denominators. They're different! So, what do we do?

We need to find a common denominator. The easiest way to do this is to find the least common multiple (LCM) of the two denominators. The LCM is the smallest number that both denominators can divide into evenly. In our case, we need the LCM of 17 and 2. Since 17 is a prime number (it’s only divisible by 1 and itself), the LCM of 17 and 2 is simply their product: 17 * 2 = 34.

Now, we need to convert both fractions to have this new denominator of 34. To do this, we multiply both the numerator and the denominator of each fraction by the number that will make the denominator 34.

For 15/17: We need to multiply the denominator 17 by 2 to get 34, so we multiply both the numerator and the denominator by 2: (15 * 2) / (17 * 2) = 30/34.

For 13/2: We need to multiply the denominator 2 by 17 to get 34, so we multiply both the numerator and the denominator by 17: (13 * 17) / (2 * 17) = 221/34.

Now we have two fractions with the same denominator: 30/34 + 221/34. This is the moment we've been waiting for! To add fractions with the same denominator, we simply add the numerators and keep the denominator the same:

  • 30 + 221 = 251

So, 30/34 + 221/34 = 251/34. We've done it! We've added the fractions. But, we're not quite finished yet. Our answer is an improper fraction (the numerator is larger than the denominator). Let's convert it back to a mixed number to make it easier to understand.

Converting Back to a Mixed Number and Final Answer

We've arrived at the fraction 251/34, which is the result of our addition. However, as we discussed earlier, it’s often more convenient and easier to understand the value if we convert this improper fraction back into a mixed number. So, how do we do that?

To convert an improper fraction to a mixed number, we perform division. We divide the numerator (251) by the denominator (34). The quotient (the whole number result of the division) will be the whole number part of our mixed number, the remainder will be the numerator of the fractional part, and the denominator stays the same.

Let's divide 251 by 34:

  • 251 ÷ 34 = 7 with a remainder of 13.

This tells us that 251/34 is equal to 7 whole times with 13 left over, which becomes the numerator of our fraction, and we keep the original denominator 34. So, 251/34 converted to a mixed number is 7 13/34.

And there we have it! We’ve successfully navigated our way through the entire problem. Our final answer to the question 5/17 * 3 + 6 1/2 is 7 13/34. Woohoo! Give yourselves a pat on the back – you've earned it!

Converting back to a mixed number is like putting the finishing touches on a masterpiece. It makes the answer more relatable and easier to visualize. Instead of just seeing 251/34, we can now see 7 13/34, which gives us a clearer sense of the value. This skill is particularly useful in real-world situations, like when you're measuring ingredients for a recipe or figuring out how much material you need for a project. It's all about making the math meaningful and practical. So, congratulations on reaching the end of this mathematical journey! You’ve not only solved the problem but also reinforced some essential math skills along the way.

Conclusion

So, guys, we've successfully solved the problem 5/17 * 3 + 6 1/2! We broke it down step-by-step, from understanding the order of operations (PEMDAS) to converting mixed numbers, performing multiplication, adding fractions, and finally, converting back to a mixed number. Remember, math is like building with LEGOs – each skill builds upon the others. By mastering these fundamental concepts, you're setting yourself up for success in more complex math problems. Keep practicing, stay curious, and never be afraid to ask questions. You've got this! Math can be challenging, but it's also incredibly rewarding when you crack the code. And who knows, maybe you'll even start to enjoy it (gasp!). Keep up the awesome work, and I'll catch you in the next math adventure!