Solving (2*(-6)) ÷ (-24) ÷ 8 * 12 A Step-by-Step Guide

Hey guys! Ever stumbled upon a math problem that looks like a jumbled mess of numbers and operations? Well, you're not alone! Today, we're going to break down a seemingly complex expression step-by-step, so you can conquer similar problems with confidence. Our mission? To solve (2*(-6)):(-24):8)*12. Sounds intimidating, right? But trust me, with a little bit of order of operations know-how, we'll have this cracked in no time. Let's dive in and make math a little less scary, one step at a time. We'll take you through each calculation, explaining the logic behind every move. Think of this as your friendly guide to mathematical mastery. Ready to get started? Let's go!

Understanding Order of Operations (PEMDAS/BODMAS)

Before we even think about touching the problem, let's quickly recap the golden rule of math: order of operations. You might have heard of it as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). Basically, it tells us the sequence in which we should perform calculations to get the right answer. It's like a mathematical traffic law, ensuring everyone arrives at the same destination. So, remember, PEMDAS/BODMAS is our trusty guide! In our equation, (2*(-6)):(-24):8)*12, we'll first tackle any parentheses, then multiplication and division (from left to right), and finally, we'll worry about addition and subtraction (though we don't have any of those here). Mastering this order is super crucial for getting accurate results. Imagine if we just went from left to right without a plan – we'd end up with a completely different, and incorrect, answer! It's like trying to build a house without a blueprint; things are bound to go wrong. So, always keep PEMDAS/BODMAS in the back of your mind, and you'll be a math whiz in no time.

Step 1: Solving the Parentheses (2 * -6)

The first step in our mathematical adventure, guided by the all-powerful PEMDAS/BODMAS, is to tackle those parentheses! We've got (2 * -6) staring right at us, begging to be solved. This is a straightforward multiplication: a positive 2 multiplied by a negative 6. Remember the rule: a positive times a negative equals a negative! So, 2 * -6 equals -12. Boom! We've conquered the first hurdle. Now, we can replace (2 * -6) in our original equation with -12. Our equation now looks like this: -12:(-24):8)*12. See how much simpler it's becoming already? This is the beauty of breaking down complex problems into smaller, manageable steps. It's like eating an elephant – you wouldn't try to swallow it whole, right? You'd take it one bite at a time. Similarly, in math, we take one operation at a time, focusing our energy and ensuring accuracy. And trust me, mastering these smaller steps is the key to tackling bigger, scarier problems down the road. So, let's keep going, one step at a time, and watch as this mathematical beast turns into a purring kitten!

Step 2: Division from Left to Right (-12 ÷ -24)

Alright, let's keep the ball rolling! Now that we've handled the parentheses, it's time to tackle the next operation in our equation: -12:(-24):8)*12. According to PEMDAS/BODMAS, we deal with division and multiplication from left to right. So, the first division we encounter is -12 divided by -24. Here's another important rule to remember: a negative divided by a negative equals a positive! So, -12 / -24 becomes a positive fraction. To simplify things, we can think of this as 12/24. Now, both 12 and 24 are divisible by 12, so we can simplify this fraction to 1/2 or 0.5. Awesome! We've just cleared another hurdle. Now, let's update our equation. Replacing -12:(-24) with 0.5, we get: 0.5:8)*12. See how the equation is gradually transforming from a jumbled mess into something much cleaner and easier to handle? This is the power of methodical problem-solving. We're not just blindly crunching numbers; we're strategically simplifying the equation step-by-step. This approach not only helps us get the right answer but also builds our understanding of the underlying mathematical principles. So, let's keep this momentum going and move on to the next step!

Step 3: Continuing the Division (0.5 ÷ 8)

Okay, mathletes, we're on a roll! Our equation is now looking much friendlier: 0.5:8)*12. We've already conquered the parentheses and the first division. Now, it's time to tackle the next division: 0.5 divided by 8. This might seem a little trickier than the previous one, but don't worry, we've got this! We can think of 0.5 as one-half (1/2). So, we're essentially dividing one-half by 8. Remember the rule for dividing fractions? We multiply by the reciprocal! So, dividing by 8 is the same as multiplying by 1/8. Therefore, 0. 5 / 8 is the same as (1/2) * (1/8), which equals 1/16. If we want to express this as a decimal, 1/16 is equal to 0.0625. Phew! That's another operation down. Let's update our equation once more. Replacing 0.5:8 with 0.0625, we now have: 0.0625 * 12. We're getting closer and closer to the finish line! Each step we take not only brings us closer to the solution but also reinforces our understanding of mathematical operations. It's like building a muscle – the more we exercise it, the stronger it gets. So, let's keep flexing our math muscles and tackle that final multiplication!

Step 4: Final Multiplication (0.0625 * 12)

Drumroll, please! We've reached the final step in our mathematical journey. Our equation has been whittled down to a single operation: 0.0625 * 12. This is the home stretch, guys! Let's bring it home. This is a straightforward multiplication problem. If you're comfortable with decimal multiplication, you can simply multiply 0.0625 by 12. If you prefer, you can think of 0.0625 as the fraction 1/16 (which we calculated in the previous step). So, we're essentially multiplying 1/16 by 12. This can be written as (1/16) * 12, which is the same as 12/16. Now, we can simplify this fraction by dividing both the numerator (12) and the denominator (16) by their greatest common divisor, which is 4. So, 12/16 simplifies to 3/4. And what is 3/4 as a decimal? You guessed it: 0.75! So, whether you multiplied the decimals directly or worked with fractions, we arrive at the same answer: 0.0625 * 12 = 0.75. Ta-da! We've done it! We've successfully solved the equation (2*(-6)):(-24):8)*12. This final step is a testament to the power of breaking down a complex problem into smaller, manageable steps. And more importantly, it's proof that you, my friend, are a math-solving superstar!

Conclusion: We Did It!

Woohoo! Give yourselves a pat on the back, guys! We've successfully navigated the mathematical maze and emerged victorious. We started with a seemingly daunting equation: (2*(-6)):(-24):8)*12, and through the magic of order of operations (PEMDAS/BODMAS) and a step-by-step approach, we arrived at the answer: 0.75. Isn't it amazing how a complex problem can become so much simpler when broken down into smaller pieces? We conquered parentheses, mastered division, and aced multiplication. We learned (or re-learned) the importance of following the order of operations and the power of simplifying fractions. But more than just getting the right answer, we've hopefully gained a deeper appreciation for the beauty and logic of mathematics. Remember, math isn't about memorizing formulas; it's about understanding concepts and applying them strategically. So, the next time you encounter a challenging math problem, don't panic! Take a deep breath, remember our step-by-step approach, and unleash your inner math whiz. You've got this! And remember, practice makes perfect. The more you practice, the more comfortable and confident you'll become in your math abilities. So, keep exploring, keep learning, and keep solving! And until next time, happy calculating!