Solving 12/2/2 + 2 * 101 + √4 + 24 ÷ 60 A Step-by-Step Guide

Hey guys! Today, we're diving into a fun mathematical equation: 12/2/2 + 2 * 101 + √4 + 24 ÷ 60. It looks a bit intimidating at first glance, but don't worry, we'll break it down step by step. Think of it like this – we're going on a mathematical adventure together, and by the end, we'll have conquered this beast of an equation! We'll explore the order of operations, tackle division, multiplication, square roots, and even a bit of fractions. So, buckle up, grab your calculators (or your mental math skills!), and let's get started! We'll make sure to explain every step clearly, so even if math isn't your favorite subject, you'll be able to follow along and understand the process. By the time we're done, you'll not only have the answer, but you'll also have a better understanding of how to approach similar mathematical problems in the future. Isn't that awesome? Let's transform this equation from a scary jumble of numbers and symbols into a clear, understandable solution. We'll use a method called PEMDAS (or BODMAS, depending on where you learned math), which is like our trusty map for navigating the world of mathematical operations. It tells us exactly which operations to perform in what order, ensuring we arrive at the correct destination – the solution! So, are you ready to become a mathematical equation-solving pro? Let's do this!

Understanding the Order of Operations (PEMDAS/BODMAS)

Before we even think about punching numbers into a calculator, we need to understand the golden rule of math equations: the order of operations, often remembered by the acronyms PEMDAS or BODMAS. Think of it as the secret code to unlocking the solution. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). BODMAS is similar: Brackets, Orders (exponents and roots), Division and Multiplication (from left to right), and Addition and Subtraction (from left to right). Both essentially guide us to solve the equation in the correct sequence. Why is this so important, you ask? Well, imagine trying to bake a cake without following the recipe. You might end up with a delicious mess, but it probably won't be the cake you were hoping for. Similarly, if we don't follow the order of operations, we'll likely end up with the wrong answer. It's like trying to build a house starting with the roof – it just won't work! So, let's break down PEMDAS/BODMAS a bit further. First, we tackle anything within parentheses or brackets. These are like VIP sections in our equation, getting priority treatment. Next come exponents and orders (like square roots). These show us how many times to multiply a number by itself, or the opposite – finding the number that, when multiplied by itself, equals another number. Then, we handle multiplication and division. Here's a crucial point: we perform these operations from left to right, as they appear in the equation. This is where many people stumble, so pay close attention! Finally, we deal with addition and subtraction, again working from left to right. By following this order, we ensure that we're solving the equation in the mathematically correct way. It's like having a GPS for our math journey, guiding us step-by-step to the final answer. So, with PEMDAS/BODMAS firmly in our minds, let's return to our equation and see how this order of operations helps us solve it.

Step-by-Step Solution: 12/2/2 + 2 * 101 + √4 + 24 ÷ 60

Alright, let's get our hands dirty and solve this equation, applying our newfound knowledge of PEMDAS/BODMAS! Our equation is 12/2/2 + 2 * 101 + √4 + 24 ÷ 60. Remember, we need to go through the order of operations systematically. First up, are there any parentheses or brackets? Nope, we're clear on that front. Next, we look for exponents or orders, which include square roots. We've got one: √4. The square root of 4 is 2 because 2 multiplied by itself (2 * 2) equals 4. So, we can replace √4 with 2 in our equation. Now, our equation looks like this: 12/2/2 + 2 * 101 + 2 + 24 ÷ 60. Moving on to the next step, we handle multiplication and division, working from left to right. We have 12/2/2. This is where things can get a little tricky if we don't remember the left-to-right rule. We first divide 12 by 2, which gives us 6. Then, we divide 6 by 2, which results in 3. So, 12/2/2 = 3. Now, let's tackle the other multiplication and division operations. We have 2 * 101, which equals 202. And we have 24 ÷ 60. This is a division that results in a fraction or decimal. 24 divided by 60 is 0.4. So, our equation now looks like this: 3 + 202 + 2 + 0.4. We're in the home stretch! The last step is addition and subtraction, again working from left to right. We simply add all the numbers together: 3 + 202 + 2 + 0.4 = 207.4. And there you have it! The solution to the equation 12/2/2 + 2 * 101 + √4 + 24 ÷ 60 is 207.4. We successfully navigated through the operations, followed the rules of PEMDAS/BODMAS, and arrived at our final answer. This step-by-step approach not only helps us solve the equation correctly but also deepens our understanding of how mathematical operations work together. It's like building a strong foundation for more complex mathematical challenges in the future. So, let's celebrate this small victory and move on to discussing why this order of operations is so crucial.

Why the Order of Operations Matters

You might be thinking,