Math Problem: Fractions, Division, And Mixed Numbers
Hey guys! Let's dive into a fun little math problem. We're going to simplify an expression involving fractions, division, and a bit of order of operations. The goal is to get a final answer that's either a proper fraction or a mixed number. Ready to get started? Let's break it down step-by-step to make sure we get it right. It's like a puzzle, and the final answer is the key! This problem is a great way to brush up on your skills with fractions and mixed numbers. Let's make sure our math skills are on point. This type of problem is designed to test your understanding of order of operations, fractions, and how to convert between different forms of numbers. We will go through the steps methodically to make it super easy to follow along. Remember, mastering the fundamentals of math is like building a strong foundation for a house â it supports everything else you do! Are you ready to level up your math game? Let's jump in and crush this problem together!
Understanding the Problem: The Core Components
Okay, so the initial expression we're working with is: 1/10 + 4 : 1 - 1/2. Seems simple enough, right? But don't let it fool you â there are a few important things to keep in mind. First off, we've got fractions. We'll need to remember how to add and subtract them. Second, there's division. Remember that division and fractions are related â they're two sides of the same coin, really! Third, we've got the order of operations. This is absolutely critical. Remember the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)? It tells us the exact order in which we need to tackle the different parts of the problem. This means that we do division before addition and subtraction. Getting this right is super important; otherwise, we'll end up with the wrong answer! The fractions might seem intimidating at first, but with a little practice, they become like second nature. Trust me; they are your friends in the world of math. Keep these concepts in mind as we go through each step. We'll be using these building blocks to get our final solution. Let's make sure we're on the right track! Take a deep breath; this is easier than it looks.
Breaking Down the Expression: Step by Step
Alright, let's get into the nitty-gritty and work through the problem step by step. Following PEMDAS, our first move is to deal with the division part: 4 : 1. Any number divided by 1 is the number itself. So, 4 : 1 is simply 4. Now our expression looks like this: 1/10 + 4 - 1/2. Next up, we have addition and subtraction. Let's tackle them from left to right. But before we can add or subtract fractions, we need to make sure they have a common denominator. In our case, we have 1/10 and 1/2. The easiest common denominator here is 10. To turn 1/2 into a fraction with a denominator of 10, we multiply both the numerator and the denominator by 5, which gives us 5/10. Now, our expression looks like this: 1/10 + 4 - 5/10. Remember, when adding or subtracting fractions, only the numerators change. The denominator stays the same. Keep your eye on the ball here, and stay focused. Don't worry, we are almost there. We will now perform the addition and subtraction, which is where things become a bit more interesting, but don't worry, we will conquer this step together!
Adding and Subtracting Fractions and Whole Numbers
Now, letâs add 1/10 and the whole number, 4. To do that easily, let's think of 4 as 4/1. But before we get ahead of ourselves, let's keep things straight: 1/10 + 4 - 5/10. We have to address the whole number before we proceed. We can represent 4 as 4/1, but to add or subtract it from the fractions, we need a common denominator. That's why it is really important to know your multiplication tables. The common denominator here will be 10. We need to convert 4/1 into an equivalent fraction with a denominator of 10. To do that, we multiply both the numerator and the denominator by 10, giving us 40/10. So our expression now looks like this: 1/10 + 40/10 - 5/10. Now, we can comfortably add and subtract the fractions. Adding 1/10 and 40/10 gives us 41/10. Then we subtract 5/10 from 41/10, which gives us 36/10. Are you still with me? Great! We are on the final stretch! Remember that we are aiming for the final answer to be a proper fraction or a mixed number. We can simplify our fraction by dividing the numerator and denominator by their greatest common factor, which is 2. Therefore, 36/10 simplifies to 18/5. This is an improper fraction (the numerator is larger than the denominator), so we can convert it into a mixed number. Dividing 18 by 5 gives us 3 with a remainder of 3. So, 18/5 as a mixed number is 3 3/5. And there we have it, guys! The solution.
Final Answer and Conclusion
So, the final answer, expressed as a mixed number, is 3 3/5. Congratulations, you've successfully worked through the problem! You've navigated fractions, division, and the order of operations. You should be proud of yourself. This is an awesome achievement! Remember the key steps: follow the order of operations, find common denominators when adding and subtracting fractions, and simplify your answers whenever possible. Keep practicing these types of problems, and you'll become a fraction master in no time! Mastering math takes time and practice. Don't worry if it doesnât click immediately. The key is to keep at it! Do more problems and ask questions if you get stuck, and youâll see yourself getting better and better. Keep up the great work and the momentum! You've got this! Now, go celebrate your success! Well done, everyone!