Mastering Math Equations A Step-by-Step Guide

Jul 17, 2025 by ADMIN 46 views

Unlocking Mathematical Mysteries A Step-by-Step Guide to Solving Equations

Hey guys! Math can sometimes feel like unlocking a secret code, right? But don't worry, we're going to break down some equations together and make it super easy to understand. We'll take it step by step, so you can follow along and become a math whiz in no time. Let's dive into some interesting mathematical problems and solve them together!

2. 56 + 8 + 2 × 6

Okay, let's kick things off with our first equation: 56 + 8 + 2 × 6. Now, remember the golden rule in math – order of operations! You might have heard of PEMDAS or BODMAS. It's basically the secret recipe for solving equations. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). BODMAS is similar: Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right). We need to follow this order to get the correct answer. So, where do we start?

First up, we've got multiplication. We see 2 × 6, and that equals 12. So, we can rewrite our equation as: 56 + 8 + 12. See? We're already simplifying things! Now, we just have addition left. We can add these numbers from left to right. So, 56 + 8 equals 64. Now our equation looks even simpler: 64 + 12. And finally, 64 + 12 gives us 76. Ta-da! We've solved the first equation. The answer is 76.

To really grasp this, let's think about why the order of operations is so important. Imagine if we just added everything from left to right without considering multiplication first. We would get a totally different (and incorrect) answer. By following PEMDAS/BODMAS, we ensure everyone solves the equation the same way and gets the same correct result. It's like a universal math language that everyone understands. So, always keep PEMDAS/BODMAS in mind, and you'll be golden!

Now, let's recap. We started with 56 + 8 + 2 × 6. We identified the multiplication operation first (2 × 6 = 12). Then, we rewrote the equation as 56 + 8 + 12. Finally, we performed the additions from left to right: 56 + 8 = 64, and 64 + 12 = 76. So, our final answer is 76. Great job! You've tackled the first equation like a pro.

3. 90 + 2 × (4 + 16)

Alright, let's move on to our next challenge: 90 + 2 × (4 + 16). This one has parentheses, so we know where to start according to our trusty PEMDAS/BODMAS rule. Remember, Parentheses (or Brackets) come first. So, we need to solve what's inside the parentheses before we do anything else. What do we have inside? (4 + 16). Easy peasy, 4 + 16 equals 20. Now, let's rewrite our equation with this simplification: 90 + 2 × 20.

See how much cleaner it looks already? Now, looking at our new equation, what's the next operation we should tackle? You guessed it – multiplication! We have 2 × 20. What's that? It's 40! So, let's replace that in our equation: 90 + 40. We're almost there! Now, we just have one simple addition problem to solve. 90 + 40 is… 130! Boom! We've cracked the code. The answer to the equation 90 + 2 × (4 + 16) is 130.

This problem really highlights the power of PEMDAS/BODMAS. If we had ignored the parentheses and just gone from left to right, we would have ended up with a completely different answer. Parentheses are like VIP sections in math – they get priority treatment. So, always make sure to handle them first. It's like making sure you have your directions straight before starting a road trip – it saves you from getting lost!

Let's break down the steps again to solidify our understanding. We began with 90 + 2 × (4 + 16). We addressed the parentheses first: (4 + 16) = 20. This transformed our equation into 90 + 2 × 20. Next, we handled the multiplication: 2 × 20 = 40. This left us with 90 + 40. Finally, we performed the addition: 90 + 40 = 130. So, our final answer is 130. You're doing amazing! You're mastering these equations one step at a time.

4. 16 + 4 × 3 - 4

Okay, let's jump into our next equation: 16 + 4 × 3 - 4. We're getting the hang of this PEMDAS/BODMAS thing, right? So, let's think… what comes first? There are no parentheses or exponents here, so we move on to Multiplication and Division. We spot a multiplication operation: 4 × 3. What does that equal? That's right, it's 12. So, we rewrite our equation as: 16 + 12 - 4. Looking good!

Now, we have addition and subtraction left. Remember, we tackle these from left to right. So, first, we do 16 + 12. What's that? It's 28. Now our equation is even simpler: 28 - 4. And finally, 28 - 4 gives us 24. We did it! The answer to 16 + 4 × 3 - 4 is 24. See how following the order of operations makes everything so clear and straightforward?

Think about it this way: the order of operations is like the grammar of mathematics. Just like grammar helps us understand sentences, PEMDAS/BODMAS helps us understand equations. Without it, things can get confusing and lead to misinterpretations. Imagine reading a sentence where the words are all jumbled up – it would be hard to make sense of it, right? The same goes for math. The order of operations gives structure and clarity to our calculations.

Let's quickly review the steps we took. We started with 16 + 4 × 3 - 4. We identified the multiplication first: 4 × 3 = 12. We rewrote the equation as 16 + 12 - 4. Then, we performed addition and subtraction from left to right: 16 + 12 = 28, and 28 - 4 = 24. So, our final answer is 24. You're crushing it! You're becoming a true equation-solving expert.

5. (32 + 2 - 4) × 7

Alright, let's tackle our final equation for today: (32 + 2 - 4) × 7. This one has parentheses again, so we know that's our starting point, thanks to PEMDAS/BODMAS. Inside the parentheses, we have 32 + 2 - 4. We've got addition and subtraction, so we tackle them from left to right. First up, 32 + 2 equals 34. Now we have 34 - 4. That's easy! It's 30. So, we've simplified the expression inside the parentheses to 30. Let's rewrite our equation: 30 × 7.

Now, we just have one simple multiplication problem to solve. What's 30 × 7? Think about it… It's like having 3 groups of 7, but ten times bigger. 30 × 7 is 210! Woohoo! We've solved the final equation. The answer to (32 + 2 - 4) × 7 is 210. You've conquered all the equations we set out to solve today. Give yourself a pat on the back!

This equation really emphasizes how important it is to work step by step. By breaking down the problem into smaller, manageable chunks, we made it much easier to solve. It's like climbing a staircase – you take it one step at a time, and before you know it, you've reached the top. Math is the same way. Each step we take gets us closer to the solution. And by following the order of operations, we ensure that each step is correct.

Let's do one last recap to really nail this down. We started with (32 + 2 - 4) × 7. We tackled the parentheses first, working from left to right: 32 + 2 = 34, and then 34 - 4 = 30. This simplified our equation to 30 × 7. Finally, we performed the multiplication: 30 × 7 = 210. So, our final answer is 210. You've aced it! You've demonstrated a solid understanding of the order of operations and how to solve equations effectively.

Wrapping Up

Awesome job, everyone! You've successfully navigated through a bunch of equations, and you've become total pros at using the order of operations (PEMDAS/BODMAS). Remember, math might seem tricky at first, but by breaking it down into smaller steps and following the rules, you can conquer any problem. Keep practicing, keep exploring, and most importantly, keep having fun with math! You've got this!