Solving Math Problems: Sıra Sizde 7. Question

Hey everyone, let's dive into a cool math problem! Today, we're tackling a question from the "Sıra Sizde" series, specifically the 7th problem. The problem involves fractions, subtraction, and a bit of division. Ready to break it down? The question is: Find the result of the operation 4/3 - 5/2 ÷ 10/6. It might look a little intimidating at first glance, but trust me, we'll break it down step by step. This is a fantastic opportunity to refresh our understanding of how to work with fractions and the order of operations. So, grab your pencils, or your favorite digital drawing tools, and let's get started. This problem is a great way to sharpen your skills, no matter your current math level. We'll focus on clarity, ensuring that everyone, from math wizards to those who find fractions a bit tricky, can follow along. We'll start by making sure we're all on the same page with the fundamentals, then we'll gradually work our way through the problem, making sure we understand each step.

Understanding the Problem: Fractions and Order of Operations

So, before we get into the nitty-gritty of the calculations, let's make sure we're clear on the basics. This problem uses fractions, which represent parts of a whole. For example, 4/3 means we have four parts out of a whole that is divided into three equal parts. The key to successfully solving this problem lies in understanding the order of operations – often remembered by the acronym PEMDAS or BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction). This tells us the sequence in which we should perform the calculations. In our case, we have subtraction and division. According to the order of operations, we need to handle the division part before we do the subtraction. Think of it like a recipe: you wouldn't add the salt before you finish preparing the main ingredients. Therefore, our first step is to deal with the division: 5/2 ÷ 10/6. It's crucial to get this right to avoid making common mistakes. Always remember that in math, there's a specific order for everything, and it's there to make sure we get the same answers, every time. Getting the order of operations down is one of the most fundamental, and easily mastered, concepts in math. Once we've done the division, we'll be able to tackle the subtraction part of the problem.

Step-by-Step Solution: Breaking Down the Math

Alright, let's get our hands dirty and work through this math problem step-by-step! First things first, let's tackle the division: 5/2 ÷ 10/6. When dividing fractions, we actually flip the second fraction (the divisor) and multiply. So, 5/2 ÷ 10/6 becomes 5/2 * 6/10. Now, we multiply the numerators (the top numbers) and the denominators (the bottom numbers). This means we multiply 5 by 6, and 2 by 10. This gives us (5 * 6) / (2 * 10) = 30/20. Now, let's simplify this fraction. Both the numerator and denominator are divisible by 10, so we divide both by 10. This simplifies to 3/2. So, the result of the division is 3/2. Now that we have solved the division part, we can move on to the main operation, which is the subtraction. The original equation was 4/3 - 5/2 ÷ 10/6, which simplifies to 4/3 - 3/2. To subtract these fractions, we need a common denominator. The easiest way to find this is to look for the least common multiple (LCM) of the denominators, which are 3 and 2. The LCM of 3 and 2 is 6. So, we will convert both fractions to have a denominator of 6. For 4/3, we multiply both the numerator and the denominator by 2, which gives us 8/6. For 3/2, we multiply both the numerator and the denominator by 3, which gives us 9/6. Now, we can perform the subtraction: 8/6 - 9/6. Subtracting the numerators gives us (8 - 9)/6 = -1/6. Therefore, the final answer to the problem 4/3 - 5/2 ÷ 10/6 is -1/6.

Final Answer and Key Takeaways

So, after breaking down the problem step by step, we have arrived at our final answer: -1/6. Not so tough, right? The key takeaways from this problem are the importance of understanding the order of operations and the ability to work with fractions, including division, multiplication, and subtraction. Remember to always flip and multiply when dividing fractions, and don't forget to find a common denominator when adding or subtracting them. Make sure that you simplify the fractions at the end. Understanding these concepts is vital for success in all areas of mathematics. Now, how about we recap the steps? First, address the division by inverting and multiplying. Simplify the fraction. Find the common denominator. Subtract the fractions. Double-check the answer. That might seem like a lot, but with practice, it'll become second nature. Keep practicing, and you'll find that solving math problems becomes much easier. This is a great example of how breaking down a problem into smaller, manageable steps can make even complex equations solvable. Keep up the great work, and keep practicing! Remember, practice makes perfect. The more you solve problems like this, the better you'll become at them. The beauty of math is that it's a skill you can improve with dedication and effort. Congratulations on solving this math problem – you've done great!