Calculating 2/3 * 1 4/5: A Step-by-Step Guide

Hey guys! Let's dive into a super common math problem: multiplying fractions and mixed numbers. Specifically, we're tackling how to calculate 2/3 multiplied by 1 4/5. It might seem a little tricky at first, but trust me, once you break it down, it's totally manageable. We'll go through each step, so you’ll be a pro in no time. Understanding fractions and mixed numbers is super important, especially when you're dealing with everyday situations like cooking, measuring, or even splitting a pizza! This guide is designed to make the process clear and easy, so let's get started and make math a little less intimidating and a lot more fun.

Understanding the Basics: Fractions and Mixed Numbers

Before we jump into the calculation, let's make sure we're all on the same page with the basics. First up, fractions. A fraction represents a part of a whole. It's written as two numbers, one on top of the other, separated by a line. The top number is called the numerator, and it tells you how many parts you have. The bottom number is the denominator, and it tells you how many parts make up the whole. For example, in the fraction 2/3, 2 is the numerator, and 3 is the denominator. This means we have 2 parts out of a total of 3.

Next, let's talk about mixed numbers. A mixed number is a combination of a whole number and a fraction. Our problem includes the mixed number 1 4/5. This means we have one whole and 4/5 of another whole. Mixed numbers can sometimes look a bit intimidating, but they're actually super useful in real-life situations. Think about measuring ingredients for a recipe – you might need 1 1/2 cups of flour, for example. So, it’s crucial to know how to work with them. To make things easier for multiplication, we'll need to convert this mixed number into an improper fraction. Don't worry, it's not as scary as it sounds! We'll cover that in the next section. By understanding these basics, we set ourselves up for success in solving the problem. So, let's move on to the next step and get that mixed number ready for action!

Converting Mixed Numbers to Improper Fractions

Okay, so we've got our mixed number, 1 4/5, and the first thing we need to do is turn it 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). Why do we need to do this? Well, it makes multiplying fractions way easier. Trust me on this one!

Here’s how we convert a mixed number to an improper fraction. It’s a pretty straightforward process, so follow along: First, we're going to multiply the whole number part of our mixed number (which is 1 in this case) by the denominator of the fractional part (which is 5). So, we have 1 * 5, which equals 5. Got it? Great! Next, we're going to add the result from the previous step (which is 5) to the numerator of the fractional part (which is 4). So, we have 5 + 4, which equals 9. This new number, 9, is going to be the numerator of our improper fraction. Now, what about the denominator? Don't worry, we don't change it! The denominator stays the same as the original mixed number, which is 5. So, putting it all together, our mixed number 1 4/5 is converted into the improper fraction 9/5. See? Not too bad, right? Now that we've got this crucial step down, we're ready to tackle the main multiplication problem. Let's keep going!

Multiplying Fractions: The Simple Steps

Now for the main event: multiplying fractions! We've already converted our mixed number into an improper fraction, so we're all set to perform the multiplication. We're dealing with 2/3 multiplied by 9/5 (which is the improper fraction version of 1 4/5). The great thing about multiplying fractions is that it's super straightforward. There are no crazy rules or complicated steps – just a simple process to follow, and you'll get the right answer every time.

The key to multiplying fractions is this: you multiply the numerators (the top numbers) together, and then you multiply the denominators (the bottom numbers) together. That's it! So, in our case, we start by multiplying the numerators: 2 * 9. This gives us 18. Next, we multiply the denominators: 3 * 5. This gives us 15. So, when we multiply 2/3 by 9/5, we get 18/15. We're not quite done yet, though. Our result, 18/15, is an improper fraction (the numerator is larger than the denominator), and it can also be simplified. We'll tackle simplifying fractions in the next section, but for now, you've successfully multiplied the fractions! High five! Let's move on to simplifying our result to get it into its simplest form.

Simplifying the Resulting Fraction

Alright, we've done the multiplication and landed on the fraction 18/15. But in math, it's always a good idea to simplify your answer as much as possible. Simplifying a fraction means reducing it to its lowest terms. Basically, we want to find the smallest possible numbers for the numerator and denominator while still keeping the fraction equivalent to the original. Why do we do this? Well, it makes the fraction easier to understand and work with in the future. Plus, it's just good mathematical practice!

To simplify a fraction, we need to find the greatest common factor (GCF) of the numerator and the denominator. The GCF is the largest number that divides evenly into both numbers. So, let's think about 18 and 15. What's the largest number that divides into both of them? If you're thinking 3, you're spot on! 3 is the GCF of 18 and 15. Now, we're going to divide both the numerator and the denominator by the GCF. So, we divide 18 by 3, which gives us 6. And we divide 15 by 3, which gives us 5. That means our simplified fraction is 6/5. But wait, we're not quite done yet! 6/5 is still an improper fraction (the numerator is larger than the denominator). To make our answer even clearer, we're going to convert it back into a mixed number. Let's head to the next section to see how that's done.

Converting Improper Fractions Back to Mixed Numbers

Okay, we've simplified our fraction to 6/5, which is an improper fraction. Now, let's convert it back to a mixed number. This will give us a clearer understanding of the value of our answer. Remember, a mixed number is a whole number combined with a fraction, like the 1 4/5 we started with. Converting back to a mixed number is the final step in presenting our answer in the best possible way.

Here's how we do it: We're going to divide the numerator (6) by the denominator (5). So, how many times does 5 go into 6? It goes in 1 time. This 1 becomes the whole number part of our mixed number. Now, we need to figure out the remainder. When we divide 6 by 5, we get 1 with a remainder of 1. This remainder, 1, becomes the numerator of the fractional part of our mixed number. And just like before, the denominator stays the same, which is 5. So, putting it all together, the improper fraction 6/5 converts to the mixed number 1 1/5. And there you have it! We've successfully converted the improper fraction back to a mixed number. This is our final, simplified answer. Now, let's recap all the steps we've taken to solve this problem.

Final Answer and Recap

Okay, guys, we made it! Let's take a moment to celebrate our math skills and recap what we've done. We started with the problem 2/3 multiplied by 1 4/5. We walked through each step, and now we have our final answer. Drumroll, please…

The final answer is 1 1/5. Awesome job! Let's quickly recap the steps we took to get there. First, we understood the basics of fractions and mixed numbers. Then, we converted the mixed number 1 4/5 into an improper fraction, which gave us 9/5. Next, we multiplied the fractions 2/3 and 9/5, resulting in 18/15. We then simplified this improper fraction to 6/5. Finally, we converted the improper fraction 6/5 back into a mixed number, which gave us our final answer of 1 1/5. See? When you break it down step by step, these problems become much easier to handle.

I hope this guide has helped you understand how to multiply fractions and mixed numbers. Math can be challenging, but with a clear process and a bit of practice, you can conquer any problem. Keep practicing, and you'll become a math whiz in no time! If you have any more math questions, don't hesitate to ask. Happy calculating!