Step-by-Step Solution To 180(25)-77(150)+120(24)
Hey guys! Math can sometimes feel like navigating a maze, right? But don't worry, we're going to break down this problem 180(25)-77(150)+120(24) into super simple steps so you can solve it with confidence. Think of it as a puzzle – each step is a piece, and once we put them all together, we've got the solution! So, grab your calculators (or your mental math muscles) and let's dive in!
Understanding the Problem
Before we start crunching numbers, let's take a moment to understand exactly what we're dealing with. We have an expression that involves multiplication and subtraction, so we need to remember our order of operations (PEMDAS/BODMAS, anyone?). This means we'll tackle the multiplications first, and then we'll handle the subtraction and addition. Our expression looks like this: 180(25) - 77(150) + 120(24). See those parentheses? They're telling us to multiply the numbers inside them. So, our first task is to calculate each of these multiplication problems separately. We need to find the values of 180 multiplied by 25, 77 multiplied by 150, and 120 multiplied by 24. Once we have those individual products, we can then put them back into the original expression and perform the subtraction and addition in the correct order, moving from left to right. Remembering the order of operations is crucial in math. If we did the subtraction or addition before the multiplication, we'd end up with a totally different answer! It's like following a recipe – you need to add the ingredients in the right order to get the final dish you want. This problem might seem a bit intimidating at first glance because of the large numbers involved, but don't let that scare you. We're going to take it step by step, and each individual step is actually quite manageable. And remember, you can always use a calculator to help with the arithmetic if you need to! The important thing is to understand the process and the logic behind each step. So, with our strategy in place, let's get to the calculations and solve this problem. Are you ready? Let's do this!
Step 1: Calculate 180(25)
Okay, let's kick things off by calculating 180 multiplied by 25. This is our first multiplication problem, and we're going to break it down to make it super easy. You can do this using the standard multiplication method, or if you're feeling fancy, you can use a mental math trick! Let's walk through the standard method first. We'll start by multiplying 180 by 5. Five times zero is zero, five times eight is forty (so we write down a zero and carry over the four), and five times one is five plus the four we carried over makes nine. So, 180 times 5 is 900. Now, we need to multiply 180 by 20. We can think of this as multiplying 180 by 2 and then adding a zero at the end. One hundred eighty times two is 360, and adding a zero gives us 3600. Finally, we add the two results together: 900 plus 3600. If you add those up, you'll get 4500. So, 180 multiplied by 25 is 4500. See? Not so scary after all! Now, if you're feeling like a mental math whiz, you could also think of 25 as one-quarter of 100. So, 180 times 25 is the same as 180 times 100 divided by 4. 180 times 100 is 18000, and 18000 divided by 4 is also 4500. There are often different ways to approach a math problem, and it's cool to explore different methods to see what works best for you. Whether you use the standard multiplication method or a mental math trick, the important thing is to understand the process and arrive at the correct answer. So, we've got our first piece of the puzzle: 180(25) = 4500. Let's keep the momentum going and move on to the next multiplication!
Step 2: Calculate 77(150)
Alright, let's tackle the second part of our mathematical journey: calculating 77 multiplied by 150. This one looks a bit more challenging, but we'll use the same strategy – breaking it down into smaller, more manageable steps. Again, you can use the standard multiplication method, or if you're feeling adventurous, try a mental math technique. Let's start with the standard method. We can think of 150 as 15 multiplied by 10. So, let's first multiply 77 by 15. When we multiply 77 by 5, we get 385. Remember to write that down! Next, we multiply 77 by 10, which is simply 770. Now, we add these two results together: 385 plus 770. That gives us 1155. So, 77 times 15 is 1155. But remember, we need to multiply by 150, not just 15. So, we need to multiply 1155 by 10. This is easy – we just add a zero to the end! So, 1155 multiplied by 10 is 11550. Therefore, 77 multiplied by 150 is 11550. Phew! We got there! Now, let's think about a potential mental math approach. We could break 150 down into 100 plus 50. So, we could calculate 77 times 100 (which is easy – it's just 7700) and then calculate 77 times 50. To find 77 times 50, we can think of it as 77 times 100 divided by 2. 77 times 100 is 7700, and 7700 divided by 2 is 3850. Then, we add the two results together: 7700 plus 3850. And guess what? That also gives us 11550! It's awesome how different approaches can lead to the same answer. So, we've conquered another multiplication: 77(150) = 11550. We're making great progress! One more multiplication to go, and then we can put it all together. Let's keep going!
Step 3: Calculate 120(24)
Okay, mathletes, let's jump into the third multiplication: calculating 120 multiplied by 24. We're following the same game plan – breaking it down into manageable steps. You know the drill by now: you can use the standard multiplication method, or if you're feeling confident, give mental math a try. Let's start with the trusty standard method. We'll multiply 120 by 4 first. Four times zero is zero, four times two is eight, and four times one is four. So, 120 times 4 is 480. Now, we need to multiply 120 by 20. We can think of this as multiplying 120 by 2 and then adding a zero. 120 times 2 is 240, and adding a zero gives us 2400. Finally, we add the two results together: 480 plus 2400. If you add those up, you'll get 2880. So, 120 multiplied by 24 is 2880. Fantastic! We've nailed another multiplication. Now, let's explore a mental math strategy. We could break 24 down into 20 plus 4. We already calculated 120 times 4 in the standard method (it's 480), so we just need to calculate 120 times 20. 120 times 20 is the same as 120 times 2 with a zero added. 120 times 2 is 240, and adding a zero gives us 2400. Then, we add 480 and 2400 together, which, as we already know, equals 2880. Boom! Another way to arrive at the same correct answer. It's like having different tools in your math toolkit – you can choose the one that feels most comfortable and efficient for the job. We've successfully calculated our third and final multiplication: 120(24) = 2880. Give yourselves a pat on the back! We've completed all the individual multiplication steps, and now we're ready to bring it all together and solve the original expression. Let's move on to the final step!
Step 4: Combine the Results
Okay, math wizards, we've done the hard work! We've calculated each of the multiplication problems, and now it's time to combine our results and find the final answer. Remember our original expression? It was 180(25) - 77(150) + 120(24). We now know that 180(25) = 4500, 77(150) = 11550, and 120(24) = 2880. So, let's substitute these values back into the expression: 4500 - 11550 + 2880. Now we have a simple subtraction and addition problem. Remember the order of operations? We perform addition and subtraction from left to right. So, first, we need to calculate 4500 minus 11550. This is going to give us a negative number, which is perfectly okay! If you subtract 11550 from 4500, you get -7050. So, our expression now looks like this: -7050 + 2880. Now, we need to add 2880 to -7050. This is like combining a debt of 7050 with a credit of 2880. The result will still be negative, but the amount will be smaller. If you add 2880 to -7050, you get -4170. And that, my friends, is our final answer! We've successfully solved the expression. We started with a seemingly complex problem, but by breaking it down into smaller steps and following the order of operations, we were able to conquer it. Math is all about taking things one step at a time, and you guys absolutely crushed it. So, the solution to 180(25) - 77(150) + 120(24) is -4170. Give yourselves a huge round of applause! You've earned it.
Final Answer
So there you have it, the final answer to our mathematical adventure is -4170. We took a seemingly complex expression and broke it down into easy-to-follow steps. We conquered the multiplications, handled the subtraction and addition, and arrived at our solution. Remember, math is like building a house – you need a strong foundation (understanding the order of operations) and you need to lay each brick carefully (solving each step methodically). If you do that, you can build anything! We hope this step-by-step guide has helped you understand how to solve this type of problem. The key takeaway is to break down complex problems into smaller, more manageable parts. Don't be intimidated by large numbers or multiple operations. Just take it one step at a time, and you'll be amazed at what you can achieve. And remember, practice makes perfect! The more you practice, the more confident you'll become in your math skills. So, keep challenging yourselves, keep exploring different problem-solving strategies, and most importantly, keep having fun with math! You guys are math superstars, and we're so proud of you for tackling this problem with us. Now, go forth and conquer more mathematical challenges! And if you ever get stuck, remember this guide and the strategies we used. You've got this! Until next time, happy mathing!
