Step-by-Step Guide Solving 9×6+4×8+3×12

Hey guys! Today, we're diving into a classic math problem that combines multiplication and addition: 9 × 6 + 4 × 8 + 3 × 12. Sounds a bit intimidating at first, right? But don’t worry, we’re going to break it down step by step, making it super easy to understand. So, grab your pencils and let's get started!

Understanding the Order of Operations

Before we jump into solving this, it’s crucial to understand the order of operations. In mathematics, there's a specific order we need to follow to ensure we get the correct answer. It’s like a recipe – you need to add the ingredients in the right order to get the perfect dish! The order of operations is often remembered by the acronym PEMDAS, which stands for:

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

Think of PEMDAS as your math superhero cape – it helps you conquer any equation! In our problem, 9 × 6 + 4 × 8 + 3 × 12, we have multiplication and addition. According to PEMDAS, we need to tackle the multiplication first before we even think about adding anything. This is super important, guys, because if we did addition first, we'd end up with a totally wrong answer. Imagine trying to bake a cake by putting it in the oven before mixing the ingredients – it just wouldn’t work, would it? Math is the same way; we gotta follow the rules!

Why Order of Operations Matters

The order of operations isn't just some arbitrary rule made up to make math harder. It's actually a fundamental principle that ensures consistency and clarity in mathematical expressions. Imagine if everyone could solve equations in whatever order they felt like – we'd have chaos! The same equation could have multiple answers, and math would become completely unreliable. Think about it like this: if you're building a house, you need to lay the foundation before you put up the walls. You can't just start with the roof! The order of operations provides that foundation for mathematical calculations, ensuring that everyone arrives at the same correct answer. By adhering to PEMDAS, we're speaking a common mathematical language, ensuring that our calculations are universally understood and accurate. It’s like having a universal translator for numbers – everyone knows what we mean, and there's no confusion. So, next time you’re tackling a math problem, remember PEMDAS – your trusty guide to mathematical accuracy!

Step 1: Perform the Multiplications

Okay, now that we've got the order of operations down, let's dive into the first step: performing the multiplications. Our problem is 9 × 6 + 4 × 8 + 3 × 12, and remember, multiplication comes before addition. So, we're going to tackle each multiplication separately.

First up, we have 9 × 6. What's that, guys? If you said 54, you’re absolutely right! So, we can rewrite our equation as 54 + 4 × 8 + 3 × 12. See how we’re making progress? We've already knocked out one part of the problem.

Next, let's handle 4 × 8. This one's pretty straightforward too. Four times eight is 32, so now our equation looks like this: 54 + 32 + 3 × 12. We're getting closer and closer to the finish line!

Finally, we have 3 × 12. What do we get when we multiply three by twelve? The answer is 36. So, our equation now becomes: 54 + 32 + 36. Awesome! We've completed all the multiplications. Give yourselves a pat on the back – you’re doing great!

Breaking Down Multiplication for Clarity

Sometimes, multiplication can seem a bit abstract, especially when dealing with larger numbers. It's helpful to remember that multiplication is simply a shortcut for repeated addition. For example, 9 × 6 is the same as adding 9 together six times: 9 + 9 + 9 + 9 + 9 + 9. While this works, multiplication is much faster and more efficient. When tackling these multiplications, you can use various strategies to make it easier. You might break down the numbers into smaller parts, use your times tables, or even draw visual aids like arrays. For 4 × 8, you could think of it as four groups of eight objects, or eight groups of four. Visualizing the problem can often help solidify your understanding. Similarly, for 3 × 12, you might break 12 into 10 + 2, then multiply 3 by 10 and 3 by 2 separately, and add the results (30 + 6 = 36). This method, known as the distributive property, can be super helpful for mental math. The key is to find the strategy that works best for you and helps you feel confident in your calculations. Remember, guys, practice makes perfect, so keep working on your multiplication skills, and you'll become a multiplication master in no time!

Step 2: Perform the Additions

Alright, superstars! We've conquered the multiplications, and now we’re on to the final stage: addition. Our equation is now sitting pretty at 54 + 32 + 36. This looks much simpler than where we started, doesn't it? We’ve broken down a complex problem into something totally manageable.

Now, we just need to add these numbers together. Remember, when adding a series of numbers, we can add them in any order we like – it won't change the final result. This is called the commutative property of addition, and it’s like a superpower that makes our lives easier! So, let’s pick the easiest way to add these up.

One way we can do this is to start by adding the first two numbers: 54 + 32. What does that give us? If you said 86, you’re spot on! So, we can rewrite our equation as 86 + 36. Now we’ve just got one more addition to do.

Finally, let's add 86 + 36. This might seem a little trickier, but we can break it down. We can think of 86 as 80 + 6 and 36 as 30 + 6. Then we can add the tens together (80 + 30 = 110) and the ones together (6 + 6 = 12). Finally, we add those results (110 + 12 = 122). So, 86 + 36 = 122. Woohoo! We did it!

Strategies for Addition

Addition might seem straightforward, but there are always tricks and strategies we can use to make it even easier and more efficient. One handy method is to look for numbers that are easy to add together. For instance, in our problem, we could have noticed that 32 and 36 are relatively close to each other, and adding them first might simplify the process. Another strategy is to use mental math techniques. For example, when adding 86 + 36, you could add 4 to 86 to make it 90, then add 36 (90 + 36 = 126), and finally subtract the 4 you added earlier (126 - 4 = 122). This method of “making tens” can be super helpful for mental calculations. You can also use visual aids like number lines or even your fingers to help you add. The most important thing is to find the method that clicks with you and helps you feel confident in your calculations. And remember, guys, practice makes perfect! The more you add, the faster and more accurate you’ll become. So, keep those addition skills sharp, and you’ll be conquering math problems like a pro!

Final Answer

Drumroll, please! We've reached the end of our journey, and it's time to reveal the final answer. We started with 9 × 6 + 4 × 8 + 3 × 12, followed the order of operations, tackled the multiplications, and then added everything up. And what did we get? The final answer is 122! You guys nailed it! Give yourselves a huge round of applause. You've successfully solved a multi-step math problem by breaking it down into manageable chunks. You've shown that even seemingly complex equations can be conquered with a little bit of strategy and a whole lot of perseverance.

Checking Your Work

In mathematics, it's always a good idea to double-check your work, guys. It's like proofreading an essay – you might catch a mistake you didn't notice the first time around. There are several ways you can check your answer. One method is to simply go back through your steps and make sure you didn't make any calculation errors. Did you multiply correctly? Did you add accurately? Another approach is to use a calculator to verify your answer. This can be a quick and easy way to catch any mistakes. However, it's important not to rely solely on calculators, as you also want to develop your mental math skills. You can also try solving the problem using a different method. For instance, if you added the numbers in one order initially, try adding them in a different order to see if you get the same result. By employing these checking strategies, you can build confidence in your answers and ensure that you're always on the right track. Remember, guys, accuracy is key in mathematics, so taking the time to check your work is always a worthwhile investment.

Conclusion

So there you have it, folks! We've successfully solved 9 × 6 + 4 × 8 + 3 × 12 using a step-by-step approach. We started by understanding the order of operations (PEMDAS), then we performed the multiplications, and finally, we tackled the additions. And most importantly, we had fun while doing it! Remember, math isn’t about being a genius or memorizing formulas. It’s about understanding the rules, breaking down problems, and thinking logically. You've shown that you have the skills and the mindset to tackle any math challenge that comes your way.

Keep Practicing!

The key to mastering math, guys, is practice, practice, practice! The more you work with numbers and equations, the more comfortable and confident you'll become. Try tackling similar problems, experimenting with different strategies, and challenging yourself to think creatively. Math is like a muscle – the more you use it, the stronger it gets. Don't be afraid to make mistakes, because mistakes are often the best learning opportunities. When you get something wrong, take the time to understand why, and you'll be even better prepared next time. There are tons of resources available to help you practice, from online games and quizzes to textbooks and worksheets. Find the resources that resonate with you, and make math a regular part of your routine. And most importantly, remember to have fun! Math can be a fascinating and rewarding subject, and the more you enjoy it, the more you'll learn. So, keep exploring, keep practicing, and keep those math skills sharp!

Great job today, everyone! Keep up the awesome work, and I'll see you next time for more math adventures!