Mixed Fraction: How To Calculate 3 - 2/7/9?
Hey guys! Ever found yourself staring at a math problem that looks like a jumbled mess of numbers and fractions? Today, we're going to tackle one of those head-scratchers together: how to express 3 - 2/7/9 as a mixed fraction. It might seem intimidating at first, but trust me, we'll break it down step by step so it’s super easy to understand. So grab your pencils, and let's dive in!
Understanding the Problem: 3 - 2/7/9
Okay, so first things first, let's really understand what we're dealing with. We've got this expression: 3 - 2/7/9. Now, this isn't your typical straightforward subtraction problem because we've got fractions stacked on fractions. The key here is to realize that this actually means we're dividing 2 by 7 and then dividing the result by 9. That order of operations is super important, guys, or we'll end up with the wrong answer!
To make it clearer, we can rewrite this as 3 - (2/7) / 9. See how those parentheses help us group the fraction part? It's like saying, “Hey, let's deal with this fraction stuff first.” This is crucial for solving it correctly. If we don't handle the divisions in the right order, we could get a totally different answer, and nobody wants that!
So, to recap, before we even start doing any calculations, we need to recognize that we're not just subtracting a simple fraction. We're subtracting a fraction that involves a division within itself. This understanding is the first big step in cracking this problem. We're going to take it slow and steady, making sure we get each part right. Trust me, once you've got this down, you'll be looking at these types of problems with a whole new level of confidence. Let's move on to the next step and start unraveling this fraction!
Step-by-Step Solution
Step 1: Rewriting the Expression
Alright, let's get into the nitty-gritty! As we discussed earlier, the expression 3 - 2/7/9 can be a little confusing as it stands. So, the very first thing we need to do is rewrite it in a way that makes the order of operations crystal clear. Remember, we’re dealing with division within a fraction, so we want to make sure we handle that correctly. The best way to do this is to rewrite the expression as: 3 - (2/7) / 9
See how those parentheses make all the difference? They tell us that we need to handle the 2/7 part first before we can even think about dividing by 9. It's like putting up a little fence around that fraction, saying, “Okay, let’s take care of you first.” This is super important because division is not associative, meaning the order in which we do it matters. If we just went left to right, we'd end up with a completely different answer.
Think of it like this: if you're baking a cake and the recipe says to mix the dry ingredients before adding the wet ones, you wouldn't just throw everything in at once, right? It's the same with math. Order matters! Rewriting the expression like this isn't just about making it look nicer; it's about making sure we're following the correct mathematical procedure. So, always remember, when you see a complex fraction like this, take a moment to rewrite it with parentheses to guide your steps. It's a small change that can make a huge difference in getting the right answer. Now that we've got our expression nice and clear, we can move on to the next step: dealing with that division within the fraction.
Step 2: Dividing Fractions
Okay, so now we've got our expression looking nice and neat as 3 - (2/7) / 9. The next step is to tackle that division hiding within the fraction. We need to figure out what (2/7) / 9 actually equals. This is where our fraction division skills come into play, guys. Remember, dividing by a number is the same as multiplying by its reciprocal. If that sounds like a mouthful, don't worry, we'll break it down.
Think of 9 as the fraction 9/1. Every whole number can be written as a fraction with a denominator of 1. So, (2/7) / 9 is the same as (2/7) / (9/1). Now, to divide fractions, we flip the second fraction (the divisor) and multiply. That means we flip 9/1 to 1/9. So, our division problem turns into a multiplication problem:
(2/7) / (9/1) = (2/7) * (1/9)
See how we transformed division into multiplication? This is a super handy trick that makes dividing fractions much easier. Now, all we have to do is multiply the numerators (the top numbers) and the denominators (the bottom numbers) together.
2 * 1 = 2
7 * 9 = 63
So, (2/7) * (1/9) = 2/63. That means (2/7) / 9 is equal to 2/63. We've successfully conquered the division part of our problem! We've taken a potentially confusing fraction division and turned it into a simple multiplication. Now, we can replace (2/7) / 9 with 2/63 in our original expression. We're one step closer to solving the whole thing. Next up, we'll tackle the subtraction part. Let's keep rolling!
Step 3: Subtracting the Fraction
Alright, we're making great progress! We've simplified our expression down to 3 - 2/63. Now comes the final subtraction step. To subtract a fraction from a whole number, we need to rewrite the whole number as a fraction with the same denominator as the fraction we're subtracting. In this case, our denominator is 63, so we need to rewrite 3 as a fraction with a denominator of 63.
Think of it this way: we want to turn 3 into something over 63. To do that, we multiply 3 by 63/63. Remember, 63/63 is just equal to 1, so we're not actually changing the value of 3, just how it looks.
3 = 3 * (63/63) = (3 * 63) / 63 = 189/63
So, we've successfully rewritten 3 as 189/63. Now we can rewrite our problem as:
189/63 - 2/63
Now that we have two fractions with the same denominator, subtracting them is super easy. We just subtract the numerators and keep the denominator the same.
(189 - 2) / 63 = 187/63
And there we have it! The result of our subtraction is 187/63. But we're not quite done yet. The question asked us to express the answer as a mixed fraction, and right now, we have an improper fraction (where the numerator is larger than the denominator). So, our final step is to convert this improper fraction into a mixed fraction. Let's move on to that final conversion!
Step 4: Converting to a Mixed Fraction
Okay, we've arrived at the last stage of our journey! We've got the answer in improper fraction form: 187/63. But to truly nail the problem, we need to express this as a mixed fraction. So, how do we do that? A mixed fraction, remember, is a whole number and a proper fraction combined, like 2 1/2.
To convert 187/63 into a mixed fraction, we need to figure out how many times 63 goes into 187. This is where a little bit of division comes in handy. We're essentially trying to find out how many whole groups of 63 we can pull out of 187.
So, let's divide 187 by 63. You can do this using long division or a calculator. The result is 2 with a remainder of 61. What does this mean?
It means that 63 goes into 187 two whole times (that's our whole number part), and we have 61 left over (that's the numerator of our fraction part). The denominator stays the same, which is 63.
So, we can write 187/63 as:
2 61/63
And there you have it! We've successfully converted the improper fraction 187/63 into the mixed fraction 2 61/63. This is our final answer, guys! We've taken a somewhat complex problem and broken it down into manageable steps. Give yourselves a pat on the back!
Final Answer: 2 61/63
Woo-hoo! We made it! After tackling each step with focus and care, we've arrived at the final answer. The expression 3 - 2/7/9, when expressed as a mixed fraction, is 2 61/63. Give yourself a round of applause, guys, because that's no small feat!
Let's take a quick look back at our journey. We started by understanding the problem and recognizing the order of operations. We rewrote the expression to make it clearer, then tackled the division within the fraction. We subtracted the resulting fraction from the whole number, and finally, we converted our improper fraction into a beautiful mixed fraction. That's a lot of mathematical maneuvering, and you nailed it!
This kind of problem might seem tricky at first glance, but as we've seen, breaking it down into smaller, more manageable steps makes it totally doable. The key is to stay organized, pay attention to the details, and remember the rules of fraction operations. And most importantly, don't be afraid to tackle those challenging problems head-on. You've got the skills, and you've got the determination!
So, the next time you encounter a fraction problem that looks a bit intimidating, remember our adventure today. Remember how we took it step by step, and remember that you have the power to conquer it. Keep practicing, keep exploring, and keep having fun with math! You're all math superstars in the making! Keep up the awesome work!
