Solving 3/4 + (1/2 - 3/2) A Step-by-Step Guide For Fraction Problems

Hey guys! Let's dive into solving this fraction problem together. Fraction problems might seem tricky at first, but trust me, breaking them down step-by-step makes everything so much easier. We're tackling the expression 3/4 + (1/2 - 3/2), and we'll go through each step meticulously. Think of it like following a recipe – each step is crucial to the final delicious result! So, grab your pencils and paper, and let's get started on this mathematical adventure. We'll make sure to explain every little detail so that you not only get the answer but also understand the process. Remember, understanding the 'why' behind the 'how' is what truly matters in math. Let's turn this fraction problem from daunting to doable!

Understanding the Order of Operations

Before we even touch the fractions, it's super important to understand the golden rule of math: the order of operations. You might have heard of the acronym PEMDAS (or BODMAS in some regions). This stands for:

• Parentheses (or Brackets)
• Exponents (or Orders)
• Multiplication and Division
• Addition and Subtraction

This order tells us which operations to perform first. In our problem, 3/4 + (1/2 - 3/2), we have parentheses, so that's our starting point. We need to solve what's inside the parentheses (1/2 - 3/2) before we do anything else. Ignoring this order would be like trying to ice a cake before it's baked – it just won't work! So, let's keep PEMDAS (or BODMAS) in the back of our minds as we move forward. It's our guiding star in the world of mathematical expressions. Remember guys, this isn't just about getting the right answer this time; it's about building a solid foundation for more complex problems in the future. Understanding the order of operations is a fundamental skill that will serve you well in all your mathematical endeavors. So, let’s make sure we nail this concept down perfectly before moving on. It’s the key to unlocking more mathematical doors!

Step 1: Solving Inside the Parentheses (1/2 - 3/2)

The heart of our problem right now is what's nestled inside those parentheses: (1/2 - 3/2). To subtract fractions, a crucial first step is ensuring they have a common denominator. Luckily for us, both fractions here, 1/2 and 3/2, already share the same denominator, which is 2. This makes our life much easier! When fractions share a denominator, we can directly subtract (or add) their numerators. The numerator is the top number in a fraction, and the denominator is the bottom number. So, in this case, we have 1 as the numerator of the first fraction and 3 as the numerator of the second fraction.

Now, we simply subtract the numerators: 1 - 3. This gives us -2. We keep the common denominator, which is 2. So, (1/2 - 3/2) simplifies to -2/2. But wait, we're not quite done yet! We can simplify -2/2 further. Remember, a fraction is essentially a division problem. So, -2/2 means -2 divided by 2, which equals -1. Therefore, the expression inside the parentheses, (1/2 - 3/2), simplifies beautifully to -1. See guys? It's all about breaking it down into manageable steps. This step-by-step approach not only helps us get the right answer but also builds our confidence in tackling more complex problems. We’ve conquered the parentheses, and that's a huge step forward! So, let's take a moment to appreciate our progress and get ready for the next stage of our mathematical journey. We're doing awesome!

Step 2: Rewriting the Expression

Okay, we've successfully navigated the parentheses! Now, let's rewrite our original expression, replacing the part we just solved with its simplified value. Remember, our original problem was 3/4 + (1/2 - 3/2). We've determined that (1/2 - 3/2) is equal to -1. So, we can now rewrite the expression as 3/4 + (-1). Notice how we've neatly replaced the parentheses and the fractions inside with a single whole number. This is a fantastic example of how simplifying parts of a problem can make the whole thing seem much less intimidating. It’s like decluttering your room – once you tackle one area, the rest feels more manageable!

Rewriting the expression in this way is a crucial step because it sets us up for the final operation. We've reduced a problem involving fractions and parentheses to a simple addition problem. This is the power of step-by-step problem-solving! We’re not trying to juggle everything at once; instead, we’re taking things one piece at a time. This approach is not only effective in math but also in many areas of life. Breaking down large tasks into smaller, more achievable steps can make anything feel possible. So, let's take a moment to appreciate how far we've come. We've transformed a seemingly complex problem into a much simpler one, and we're ready to finish strong! On to the final step!

Step 3: Adding the Fractions 3/4 + (-1)

Alright guys, we're in the home stretch! We've simplified our expression to 3/4 + (-1). Now, we need to add a fraction and a whole number. The key to doing this is to remember that any whole number can be written as a fraction by placing it over a denominator of 1. So, -1 can be written as -1/1. This doesn't change the value of the number; it just changes how it looks. Now our problem looks like this: 3/4 + (-1/1). Just like before when we subtracted fractions, we need a common denominator to add them.

Currently, our denominators are 4 and 1. The least common multiple (LCM) of 4 and 1 is 4. This means we need to convert -1/1 into an equivalent fraction with a denominator of 4. To do this, we multiply both the numerator and the denominator of -1/1 by 4. This gives us (-1 * 4) / (1 * 4), which simplifies to -4/4. Now we can rewrite our problem as 3/4 + (-4/4). We have a common denominator, so we can add the numerators: 3 + (-4) = -1. We keep the common denominator, which is 4. So, our final result is -1/4.

See guys? We did it! We successfully solved the problem by breaking it down into manageable steps. We tackled the parentheses first, rewrote the expression, and then added the fractions by finding a common denominator. This step-by-step approach is the secret weapon for conquering any mathematical challenge. Remember, math isn't about memorizing formulas; it's about understanding the process and applying the right strategies. And you've just demonstrated that you have what it takes! So, give yourselves a pat on the back, and let's celebrate this mathematical victory!

Final Answer

So, after all our hard work and careful steps, we've arrived at the final answer! The solution to the expression 3/4 + (1/2 - 3/2) is -1/4. Isn't it satisfying to see how a seemingly complex problem can be solved with clear steps and a bit of patience? We started with parentheses, navigated fraction subtraction, rewrote the expression, found common denominators, and finally added the fractions. Each step was a building block, and together, they led us to the correct solution. This is the beauty of mathematics – it's like a puzzle where each piece fits perfectly when you follow the rules. And you guys nailed it!

Remember, the journey is just as important as the destination. We didn't just get the answer; we understood the process. We reinforced the order of operations, practiced fraction manipulation, and honed our problem-solving skills. These are valuable tools that you can use to tackle any mathematical challenge that comes your way. So, the next time you encounter a problem that seems daunting, remember this example. Break it down, take it one step at a time, and trust in your abilities. You've got this! And who knows, maybe you'll even start to enjoy the process of solving these mathematical puzzles. Keep practicing, keep exploring, and keep that mathematical curiosity alive! You're all doing an amazing job!