Solving 27 - (6 - 2) + 4 × 2 A Step-by-Step Guide

Aug 1, 2025 by Marta Kowalska 50 views

Unlocking the Mystery: Solving the Number Sentence 27 - (6 - 2) + 4 × 2

Hey there, math enthusiasts! Ever stumbled upon a number sentence that looks like a cryptic code? Well, fear not! We're about to break down one such puzzle together, step by step. Today's mission, should you choose to accept it, is to solve the number sentence: 27 - (6 - 2) + 4 × 2. Sounds intriguing, right? Let's dive in and unravel this mathematical mystery!

The Order of Operations: Our Guiding Star

Before we even think about crunching those numbers, we need to talk about the order of operations. This is the golden rule in the world of math, a set of instructions that tells us the precise sequence in which we should perform calculations. Think of it as a mathematical GPS, guiding us to the correct answer. The most common mnemonic to remember the order of operations is PEMDAS, which stands for:

Parentheses (and other grouping symbols)
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

Why is this order so crucial, you ask? Well, imagine what would happen if we just went ahead and performed operations in the order they appear. We'd end up with a mathematical mess! By sticking to PEMDAS, we ensure that everyone arrives at the same, correct solution, no matter who's doing the calculating. In our case of solving the number sentence below, which is 27-(6-2)+4 × 2, following the order of operations is the key to success. We'll tackle the parentheses first, then handle the multiplication, and finally, we'll take care of the subtraction and addition, moving from left to right. This systematic approach is what transforms a seemingly complex equation into a manageable and even enjoyable challenge. So, buckle up, and let's put PEMDAS into action!

Step 1: Taming the Parentheses

The very first thing that catches our eye in the number sentence 27-(6-2)+4 × 2 is the set of parentheses: (6 - 2). According to PEMDAS, parentheses are our top priority. They're like little mathematical VIPs, demanding our immediate attention. So, let's focus solely on what's inside those parentheses. We have a simple subtraction problem: 6 - 2. This is a piece of cake, right? 6 take away 2 leaves us with 4. So, we can replace the entire expression inside the parentheses with the number 4. Our number sentence now looks like this: 27 - 4 + 4 × 2. See how much simpler it's becoming already? We've conquered the first hurdle, and that's a great feeling! Remember, tackling the parentheses first isn't just an arbitrary rule; it's about respecting the structure of the equation. The parentheses group the numbers 6 and 2 together, telling us that their relationship (the subtraction) needs to be resolved before we consider how they interact with the rest of the equation. By clearing the parentheses, we're essentially setting the stage for the next act in our mathematical drama. We're now ready to move on to the next operation in the PEMDAS sequence, feeling confident and in control. Onwards and upwards, guys! The mathematical adventure continues, and we're one step closer to cracking the code of this number sentence.

Step 2: Mastering Multiplication

Alright, with the parentheses handled like pros, let's move on to the next item on our PEMDAS to-do list: Multiplication. Scanning our updated number sentence, 27 - 4 + 4 × 2, we spot a multiplication operation lurking towards the end: 4 × 2. This is where we shift our focus. Just like we zeroed in on the parentheses, we're now going to isolate this multiplication problem and solve it. What's 4 multiplied by 2? It's 8, of course! So, we can replace the 4 × 2 part of our number sentence with the number 8. Now, our equation looks even cleaner: 27 - 4 + 8. We're making fantastic progress! Why does multiplication take precedence over addition and subtraction? It all comes down to how mathematical operations are defined. Multiplication is essentially a shortcut for repeated addition. For example, 4 × 2 is the same as adding 4 to itself two times (4 + 4). By performing multiplication before addition and subtraction, we're respecting this fundamental relationship and ensuring the logical flow of our calculation. Think of it like building a house: you need to construct the walls (multiplication) before you can start decorating the interior (addition and subtraction). Each step builds upon the previous one, leading us closer to the final result. So, give yourselves a pat on the back! We've successfully navigated the multiplication hurdle, and we're now ready to tackle the final stage of our mathematical journey: addition and subtraction. Let's keep that momentum going!

Step 3: Adding and Subtracting with Finesse

Okay, mathletes, we've reached the final leg of our journey! Our number sentence, after conquering parentheses and multiplication, now stands as 27 - 4 + 8. According to PEMDAS, addition and subtraction have equal priority. This means we tackle them in the order they appear, working our way from left to right, just like reading a sentence. So, what's the first operation we encounter? It's 27 - 4. Let's do it! 27 take away 4 leaves us with 23. We can replace 27 - 4 with 23, and our number sentence becomes 23 + 8. We're almost there, guys! Now, we have a simple addition problem staring us in the face: 23 + 8. Add those two numbers together, and what do you get? The answer is 31! Congratulations, we've cracked the code! The solution to the number sentence 27 - (6 - 2) + 4 × 2 is 31. See how following the order of operations, PEMDAS, made the whole process so much smoother? By breaking down the problem into smaller, manageable steps, we avoided confusion and arrived at the correct answer with confidence. This left-to-right approach for addition and subtraction is crucial because it maintains the integrity of the equation. Changing the order could lead to a different result, throwing our whole calculation off track. So, remember, when addition and subtraction are in the mix, treat them like equals and work from left to right. Give yourselves a round of applause! You've not only solved a number sentence but also reinforced the importance of the order of operations. Now you're ready to tackle even more complex mathematical challenges!

Final Answer

Therefore, after carefully following the order of operations (PEMDAS), we have successfully solved the number sentence 27-(6-2)+4 × 2. The final answer is:

Awesome job, everyone! You've proven yourselves to be true mathematical detectives, capable of unraveling even the most perplexing number puzzles. Keep practicing, keep exploring, and never stop the quest for mathematical knowledge!