Solving Arithmetic Expressions 16 × 15 - 12 And 5.3 × 14 - 15 A Step-by-Step Guide

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Hey guys! Today, we're diving into the nitty-gritty of solving arithmetic expressions. We'll be tackling two specific problems: 16 × 15 - 12 and 5.3 × 14 - 15. Don't worry, we'll break it down step-by-step so everyone can follow along. Whether you're brushing up on your math skills or just curious about how to approach these kinds of problems, you're in the right place. Let's get started and make math a little less intimidating, shall we?

Understanding Order of Operations

Before we jump into solving our expressions, it's super crucial to understand the order of operations. Think of it as the golden rule of arithmetic – we need to follow a specific sequence to arrive at the correct answer. The most common mnemonic to remember this order is PEMDAS, which stands for:

  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

Why is this order so important? Well, imagine if we didn't have a standard order. We could end up with completely different answers for the same expression, which would be chaotic! By following PEMDAS, we ensure that everyone solves the problem in the same way, leading to a consistent and accurate result. In our expressions today, we'll be focusing on multiplication and subtraction, but understanding the full order is key for tackling more complex problems down the road.

Think of it like building a house – you wouldn't put the roof on before the walls, right? Similarly, in math, we need to perform operations in the correct order to build our way to the right answer. So, with PEMDAS in mind, let's dive into our first expression.

Solving 16 × 15 - 12

Okay, let's tackle our first expression: 16 × 15 - 12. Remember PEMDAS? It tells us that multiplication comes before subtraction. So, the first thing we need to do is multiply 16 by 15. You can do this manually or use a calculator, whichever you prefer. If you're doing it manually, you might break it down like this:

  • 16 × 10 = 160
  • 16 × 5 = 80
  • 160 + 80 = 240

So, 16 × 15 equals 240. Now we can rewrite our expression as 240 - 12. See how much simpler it looks already? We've taken the multiplication step and condensed it into a single number. This is a crucial part of the process – breaking down the problem into smaller, more manageable chunks.

Now, the final step is a straightforward subtraction. We simply subtract 12 from 240. This one's pretty easy to do in your head, but if you need to write it out, go for it! 240 minus 12 is 228. And that's our answer! 16 × 15 - 12 = 228. We've successfully solved our first expression by following the order of operations and breaking down the problem into smaller steps. Feels good, right? Now, let's move on to our second expression and see if we can apply the same principles.

Solving 5.3 × 14 - 15

Alright, let's move on to our second expression: 5.3 × 14 - 15. This one introduces a decimal, but don't let that intimidate you! We're going to use the same strategy as before: follow PEMDAS and break it down step-by-step. Just like the previous problem, multiplication comes before subtraction, so we'll start by multiplying 5.3 by 14.

Multiplying with decimals can seem a little tricky, but there are a couple of ways to approach it. One way is to ignore the decimal point initially and multiply 53 by 14. Then, we'll add the decimal point back in later. Let's do that:

  • 53 × 14 = ?
    • 53 × 10 = 530
    • 53 × 4 = 212
    • 530 + 212 = 742

Now, remember that we ignored the decimal point. Since 5.3 has one decimal place, we need to put one decimal place back into our answer. So, 742 becomes 74.2. Therefore, 5.3 × 14 = 74.2. We've successfully handled the multiplication step! This is a great example of how breaking down a problem and focusing on one part at a time can make even decimal multiplication feel manageable.

Now, we can rewrite our expression as 74.2 - 15. We're down to our final step, which is a simple subtraction. Subtracting 15 from 74.2 is pretty straightforward. We get 59.2. So, the solution to our second expression is 5.3 × 14 - 15 = 59.2. We did it! We conquered the decimal and solved the problem. See, decimals aren't so scary after all when you approach them methodically.

Comparing the Solutions

Now that we've solved both expressions, let's take a moment to compare the solutions. We found that 16 × 15 - 12 = 228, and 5.3 × 14 - 15 = 59.2. Notice how different the answers are, even though both expressions involve multiplication and subtraction. This really highlights the impact of the specific numbers involved and the importance of performing the calculations accurately. Thinking about the magnitude of the numbers can also help you sense-check your answers. For example, in the first expression, we were multiplying two relatively large numbers (16 and 15), so we expected a larger result. In the second expression, one of the numbers was smaller (5.3), so the final result was also smaller.

Comparing the solutions also reinforces the importance of the order of operations. If we had accidentally subtracted before multiplying, we would have ended up with completely different answers. So, always remember PEMDAS! By comparing these two problems, we can see how mathematical principles play out in different contexts and further solidify our understanding of arithmetic expressions.

Key Takeaways and Practice

So, what are the key takeaways from our arithmetic adventure today? Firstly, we've reinforced the critical importance of the order of operations (PEMDAS). This is the foundation for solving any arithmetic expression correctly. Remember, multiplication and division come before addition and subtraction, and parentheses and exponents take top priority.

Secondly, we've demonstrated the power of breaking down complex problems into smaller, more manageable steps. Whether it's multiplying large numbers or dealing with decimals, tackling one operation at a time makes the whole process less daunting and reduces the chance of errors. This is a strategy you can apply to all sorts of mathematical problems, not just arithmetic expressions.

Finally, we've seen the value of checking your work and comparing solutions. This helps you develop a better intuition for numbers and can catch any mistakes you might have made along the way. Math isn't just about getting the right answer; it's about understanding the process and developing your problem-solving skills.

To really solidify your understanding, the best thing to do is practice! Try solving some similar arithmetic expressions on your own. You can find plenty of examples online or in textbooks. Don't be afraid to make mistakes – that's how we learn! And remember, the more you practice, the more confident and comfortable you'll become with these concepts. Keep up the great work, guys!