Solving Fractions: Step-by-Step Calculation Guide
Hey math enthusiasts! Let's dive into a classic fraction calculation problem: 2/3 - 3/4 * 5/9. This might seem a bit intimidating at first, but trust me, with the right approach, it's totally manageable. We're going to break down this problem step by step, making sure you understand every move. This guide is designed to be super clear, even if you're just getting started with fractions. So, grab your calculators (or just your brains!) and let's get started. We will explore the order of operations, simplify fractions, and ensure accurate results. By the end, you'll be confident in tackling similar problems.
First things first, it's crucial to understand the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In our case, we don't have parentheses or exponents, so we jump straight into multiplication and division. This means we'll handle the multiplication part of the equation (3/4 * 5/9) before we touch the subtraction. This order is non-negotiable; it's the foundation of getting the right answer every time. Ignoring this rule is a surefire way to end up with the wrong result. So, keep PEMDAS in mind as we proceed, because it's the boss of this mathematical party.
Now, let's talk about the specific fractions involved. We're dealing with 2/3, 3/4, and 5/9. These are the building blocks of our problem. To successfully solve it, we must understand how to multiply and subtract these fractions. When it comes to multiplication, it's pretty straightforward: multiply the numerators (top numbers) together, and then multiply the denominators (bottom numbers) together. For subtraction, things are slightly different. We must first ensure that the fractions share a common denominator. This step is pivotal for accurate calculations.
So, as we unravel this problem, we're not just crunching numbers; we're also learning fundamental mathematical concepts. We're getting a grip on the order of operations, and we're refreshing our understanding of fractions. The goal isn't just to get an answer; it's to develop a deeper understanding of how these operations work together. With each step, you're building a stronger foundation in math. Think of this as more than just a calculation; it is a learning experience that will help you solve more complex problems in the future. Are you ready to dive into the mathematical world? Let's take it piece by piece, ensuring that everything is clear and easy to understand.
Step 1: Multiply 3/4 by 5/9
Alright, guys, let's tackle the first part of our problem: the multiplication. We're starting with 3/4 * 5/9. Remember what we talked about? For multiplication, you simply multiply the numerators (the top numbers) and the denominators (the bottom numbers). So, here's how it breaks down:
- Multiply the numerators: 3 * 5 = 15
- Multiply the denominators: 4 * 9 = 36
This gives us a new fraction: 15/36. But wait, we're not done yet! We always want to simplify fractions to their simplest form. Simplifying a fraction means reducing it to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD).
In this case, the GCD of 15 and 36 is 3. So, we divide both the numerator and the denominator by 3:
- 15 ÷ 3 = 5
- 36 ÷ 3 = 12
Therefore, the simplified form of 15/36 is 5/12. This is the result of our multiplication. We’ve successfully completed the first major step! It’s all about taking it one step at a time, making sure each piece falls neatly into place. Now that we have the product of the fractions, we're ready to move on to the next crucial step. Remember, the goal here is not just to get the answer, but to understand the process so that you can tackle similar problems with confidence. How awesome is that? We're building a strong foundation in fraction calculations. Keep going, you're doing great!
Also, if you are looking for tips, you must ensure that you are using the correct math and applying it to solve the equation. Always write the mathematical steps clearly and ensure that you use the correct mathematical operations, such as addition, subtraction, multiplication, and division. Always remember the order of operations when solving any equation. This will allow you to solve it correctly and get the proper final answer.
Step 2: Subtract 5/12 from 2/3
Okay, team, now that we've nailed the multiplication, it's time for the subtraction part. Remember, our original problem was 2/3 - (3/4 * 5/9). We've already figured out that 3/4 * 5/9 equals 5/12. So, our new problem is 2/3 - 5/12. But hold on, we can't just subtract the numerators like we did with multiplication. We need to find a common denominator first. This is crucial for adding or subtracting fractions.
A common denominator is a number that both denominators can divide into evenly. In our case, the denominators are 3 and 12. The easiest way to find the common denominator is often to list the multiples of each denominator until you find a number they both share. Let's do that:
- Multiples of 3: 3, 6, 9, 12, 15…
- Multiples of 12: 12, 24, 36…
See? The smallest number they both share is 12. So, 12 is our common denominator.
Now, we need to convert our fractions so they both have a denominator of 12. The fraction 5/12 already has the common denominator, so we only need to adjust 2/3. To change 2/3 to a fraction with a denominator of 12, we ask ourselves: