Solving Numerical Expressions A Step-by-Step Guide

Hey guys! Ever stumbled upon a numerical expression that looks like a mathematical maze? Don't worry, we've all been there! Today, we're going to break down a specific expression and solve it together, step by step. Our mission? To conquer the expression: $30-(10+2 \times 3)+6 \times 2-5=$

a) What should be solved first in this expression?

When you first glance at this mathematical equation, it might seem daunting. But, fear not! There's a secret weapon in the world of math called the order of operations, often remembered by the acronym PEMDAS (or BODMAS in some regions). This nifty rule tells us exactly which operations to tackle first, ensuring we all arrive at the same correct answer. So, what is PEMDAS/BODMAS? Let's break it down:

• Parentheses (or Brackets): Anything inside parentheses or brackets gets top priority.
• Exponents (or Orders): Next up are exponents, those little numbers that tell you to multiply a number by itself.
• Multiplication and Division: These operations are like twins, holding equal importance. We solve them from left to right.
• Addition and Subtraction: The final pair, also treated equally, and tackled from left to right.

Now, let's apply this knowledge to our expression: $30-(10+2 \times 3)+6 \times 2-5=$. Looking at the expression, we spot a set of parentheses: $(10+2 \times 3)$. According to PEMDAS, this is where our journey begins. But wait, there's more within the parentheses! We have both addition and multiplication. Which one takes precedence? Ah, PEMDAS to the rescue again! Multiplication comes before addition. Therefore, the very first operation we must solve is 2 multiplied by 3. This is the key to unlocking the rest of the expression. It's like finding the first piece of a puzzle – once we have it, the rest starts to fall into place.

Understanding the order of operations is paramount in mathematics, especially when dealing with complex expressions. Imagine if we didn't have this rule – we could end up with wildly different answers depending on the order in which we performed the calculations! PEMDAS provides a universal roadmap, ensuring that everyone, from students to mathematicians, arrives at the same solution. It's the bedrock of mathematical consistency and accuracy. By adhering to this order, we avoid confusion and ensure that our calculations are not only correct but also universally understood. This principle extends beyond simple arithmetic; it's crucial in algebra, calculus, and even computer programming, where the order of operations dictates how a program interprets and executes commands. So, mastering PEMDAS is not just about solving expressions; it's about developing a fundamental skill that will serve you well in countless areas of mathematics and beyond. It's like learning the grammar of math, allowing you to speak the language fluently and accurately. Remember, math is not just about numbers; it's about logic and structure, and PEMDAS is a cornerstone of that structure.

b) Solve the expression above and present or Discussion category:

Alright, now that we know the first step, let's roll up our sleeves and solve the entire expression. We'll take it one step at a time, making sure we follow PEMDAS like true math detectives. Our expression is $30-(10+2 \times 3)+6 \times 2-5=$.

Step 1: Tackle the multiplication within the parentheses. We identified earlier that $2 \times 3$ is the operation we need to solve first. So, $2 \times 3 = 6$. Now our expression looks like this: $30-(10+6)+6 \times 2-5=$

Step 2: Finish the parentheses. We still have the parentheses to deal with. Inside, we have $10 + 6$, which equals 16. Our expression now transforms into: $30-16+6 \times 2-5=$

Step 3: Multiplication outside the parentheses. Moving along, we encounter another multiplication: $6 \times 2$. This gives us 12. The expression now reads: $30-16+12-5=$

Step 4: Addition and Subtraction (from left to right). Now we're in the home stretch! We have a series of additions and subtractions. Remember, we solve these from left to right. First, $30 - 16 = 14$. So, our expression becomes: $14+12-5=$

Step 5: Continue Addition and Subtraction (from left to right). Next, we have $14 + 12$, which equals 26. Our expression simplifies to: $26-5=$

Step 6: The Final Subtraction. Finally, we perform the last subtraction: $26 - 5 = 21$.

Therefore, the solution to the expression $30-(10+2 \times 3)+6 \times 2-5=$ is 21!

Phew! We did it! We navigated the numerical maze and emerged victorious. Solving a mathematical expression like this is like embarking on a mini-adventure. Each step is a clue, and PEMDAS is our trusty map. By following the order of operations diligently, we can conquer even the most intimidating-looking equations. This step-by-step approach not only helps us arrive at the correct answer but also deepens our understanding of mathematical principles. It's not just about getting the right number; it's about understanding the process and the logic behind it. Think of it like building a house – you wouldn't start with the roof, would you? You need a solid foundation first, and in math, PEMDAS is that foundation. It ensures that our mathematical structures are sound and stable. Moreover, this methodical approach fosters a sense of confidence. When faced with a complex problem, knowing that you have a reliable strategy to break it down into manageable steps can be incredibly empowering. Math isn't about magic; it's about method, and by mastering these methods, we unlock our mathematical potential. So, the next time you encounter a daunting expression, remember PEMDAS, take a deep breath, and start building your solution, one step at a time. You've got this!

Discussion Category: Mathematics

This problem falls squarely into the realm of mathematics, specifically arithmetic and the order of operations. It's a fundamental concept in mathematics education, often introduced in elementary or middle school. Mastering these concepts is crucial for success in higher-level math courses, such as algebra and calculus. The problem highlights the importance of following a specific set of rules to ensure consistent and accurate results. It's a cornerstone of mathematical reasoning and problem-solving. Furthermore, this type of problem serves as a building block for understanding more complex mathematical concepts. For instance, the principles of PEMDAS are essential when working with algebraic equations, simplifying expressions, and solving for variables. Without a firm grasp of the order of operations, students may struggle with these advanced topics. Therefore, problems like this are not just about finding a numerical answer; they are about developing a crucial mathematical skill that will be applied throughout one's academic journey. It's like learning the alphabet before writing a novel – it's a foundational skill that unlocks countless possibilities. In addition to its academic relevance, understanding the order of operations has practical applications in everyday life. From calculating the cost of items on sale to understanding financial formulas, these skills are valuable in a variety of contexts. So, whether you're a student tackling homework or an adult managing finances, the principles of PEMDAS remain essential for accurate calculations and informed decision-making. It's a testament to the enduring relevance of fundamental mathematical concepts.