Step-by-Step Guide To Solving 500-(36x3)+120:(8+4)
Hey guys! Math can seem daunting sometimes, especially when you're faced with a long equation filled with different operations. But don't worry, we're going to break down this problem together, step by step, and make it super easy to understand. Today, we're tackling the equation 500 – (36 x 3) + 120 ÷ (8 + 4). This might look intimidating at first glance, but with the right approach and a little bit of PEMDAS magic, we'll solve it in no time. So grab your pencils, open your notebooks, and let's dive in!
Understanding PEMDAS/BODMAS: The Golden Rule of Math
Before we even touch the equation, let's talk about the secret weapon that will guide us through this mathematical maze: PEMDAS. Or, if you learned it a different way, BODMAS! Both of these acronyms are fantastic tools that tell us the correct order of operations. Seriously, this is the golden rule when it comes to solving equations like this one. If you try to do things out of order, you're going to end up with the wrong answer, and nobody wants that! So, what does PEMDAS/BODMAS stand for?
- Parentheses / Brackets: First things first, we need to tackle anything inside parentheses or brackets. This is like the VIP section of the equation – it gets our immediate attention.
- Exponents / Orders: Next up are exponents (like those little numbers floating in the air) or orders (which is another term for powers and roots). We handle these after parentheses/brackets.
- Multiplication and Division: Multiplication and division are on the same level of importance, so we work them out from left to right. Think of it as a race – whichever operation comes first as you read the equation from left to right is the one we do first.
- Addition and Subtraction: Just like multiplication and division, addition and subtraction share the same level of priority. We solve them from left to right as well.
With PEMDAS/BODMAS firmly in our minds, we're ready to attack our equation! Remember this acronym – it's your best friend in the world of math equations.
Step 1: Tackling the Parentheses
Okay, let's take a look at our equation again: 500 – (36 x 3) + 120 ÷ (8 + 4). The first thing PEMDAS tells us to do is handle those parentheses. We have two sets of parentheses in this equation, so let's take them one at a time. The first set is (36 x 3). This is a simple multiplication problem. What's 36 multiplied by 3? If you said 108, you're absolutely right! So, we can replace (36 x 3) with 108 in our equation. Our equation now looks like this: 500 – 108 + 120 ÷ (8 + 4). See? We're already making progress!
Now, let's move on to the second set of parentheses: (8 + 4). This one's even easier! 8 plus 4 is 12. So, we can replace (8 + 4) with 12 in our equation. Now our equation looks even simpler: 500 – 108 + 120 ÷ 12. We've successfully conquered the parentheses! Feels good, right? Remember, breaking down the problem into smaller, manageable steps is the key to success in math.
Step 2: Division Comes First
Alright, we've handled the parentheses like champs. Now, according to PEMDAS, we need to look for exponents. But guess what? There are no exponents in this equation! That means we can move on to the next step: Multiplication and Division. Remember, these two operations have equal priority, so we work them from left to right. Looking at our equation, 500 – 108 + 120 ÷ 12, the first division operation we encounter is 120 ÷ 12. So, let's tackle that. What's 120 divided by 12? It's 10! You got it. Now we can replace 120 ÷ 12 with 10 in our equation. This makes our equation even more streamlined: 500 – 108 + 10. Notice how we're making the equation simpler and simpler with each step? That's the power of following PEMDAS!
Step 3: Time for Subtraction
We're on the home stretch now, guys! We've taken care of the parentheses and the division. Now PEMDAS tells us it's time for Addition and Subtraction. Just like multiplication and division, these two operations have the same priority, and we work them from left to right. Looking at our equation, 500 – 108 + 10, the first operation we encounter is subtraction: 500 – 108. So, let's do that calculation. What's 500 minus 108? It's 392! You're doing amazing. Let's replace 500 – 108 with 392 in our equation. This gives us: 392 + 10. We're almost there!
Step 4: The Grand Finale - Addition!
Only one step left! We've conquered parentheses, division, and subtraction. Now, all that's left is addition. Our equation is now a super simple 392 + 10. This is the easy part! What's 392 plus 10? It's 402! And there you have it! We've solved the equation. The answer to 500 – (36 x 3) + 120 ÷ (8 + 4) is 402. Give yourselves a pat on the back – you've earned it!
Key Takeaways: Mastering the Order of Operations
Wow, we did it! We successfully solved a seemingly complex equation by breaking it down into manageable steps. Let's recap the key things we learned today. First and foremost, we mastered PEMDAS/BODMAS, the golden rule of math. Remember those parentheses, exponents, multiplication and division, and addition and subtraction – they're your roadmap to solving any equation. We also saw how important it is to work through the equation step by step, tackling one operation at a time. This prevents confusion and helps you avoid mistakes. And finally, we learned the importance of double-checking our work to make sure we've got the right answer. Math can be tricky, but with a systematic approach and a little bit of practice, you can conquer any equation that comes your way.
So, next time you see a long equation staring back at you, don't panic! Just remember PEMDAS/BODMAS, break it down step by step, and you'll be a math whiz in no time. Keep practicing, keep learning, and most importantly, have fun with math! You guys got this!
Practice Problems: Put Your Skills to the Test
Now that we've conquered that equation together, it's time to put your new skills to the test! Practice makes perfect, so here are a few more problems for you to try on your own. Remember to use PEMDAS/BODMAS to guide you, work step by step, and double-check your answers. Don't be afraid to make mistakes – that's how we learn! Grab a pen and paper, and let's get started:
- 100 + (25 x 2) – 80 ÷ 4
- (12 + 8) x 5 – 15 x 3
- 200 – 5 x (16 + 4) + 60 ÷ 2
Try to solve these equations using the same step-by-step method we used earlier. If you get stuck, don't worry! Go back and review the steps we took in the first example. The more you practice, the more confident you'll become in your math abilities. You can even challenge your friends and family to solve these problems with you – make it a fun math challenge! And if you want to check your answers, you can use a calculator or ask a teacher or tutor for help. The most important thing is to keep practicing and keep learning. You've got this!
