Calculate (-18-3) X 7+(-23): Step-by-Step Solution

Hey guys, ever stumbled upon a math problem that looks like a jumbled mess of numbers and operations? You're not alone! Today, we're going to break down one of those problems step by step: (-18-3) x 7+(-23). Don't worry, it's not as scary as it looks. We'll walk through it together, making sure you understand each part of the process. So, grab your thinking caps, and let's dive into the world of mathematical operations!

Understanding the Order of Operations

Before we even touch the numbers, there's a golden rule we need to remember: the order of operations. This is like the traffic light system of math, telling us which operations to tackle first. Think of it as PEMDAS, a handy acronym that stands for:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

This order is crucial because if we do things out of order, we'll end up with the wrong answer. Imagine trying to build a house by putting the roof on before the walls – it just wouldn't work! Math is the same way; we need to follow the right sequence to get the correct result. Ignoring PEMDAS is like navigating without a map – you'll likely get lost along the way.

Why Order of Operations Matters

The order of operations isn't just some arbitrary rule made up to confuse students. It's a fundamental principle that ensures mathematical expressions are evaluated consistently. Without it, the same expression could yield different results depending on who's doing the calculation. Think about it: if you and a friend calculated the same problem but followed different orders, you'd end up with different answers. This would be a huge problem in fields like engineering, finance, and science, where accurate calculations are absolutely essential. So, PEMDAS acts as a universal language, ensuring everyone is on the same page when it comes to math.

A Real-World Analogy

To further illustrate the importance of the order of operations, let's consider a real-world example. Imagine you're baking a cake. The recipe might tell you to first mix the dry ingredients, then add the wet ingredients, and finally bake the mixture. If you were to add the wet ingredients before mixing the dry ones, or try to bake the ingredients separately, you wouldn't end up with a cake! The order of steps matters in baking, just as the order of operations matters in math. Each step builds upon the previous one, leading to the final, desired result. So, always remember to follow the recipe (or PEMDAS) for success!

Breaking Down the Problem: (-18-3) x 7+(-23)

Now that we've got PEMDAS firmly in our minds, let's apply it to our problem: (-18-3) x 7+(-23). The first thing we spot are those parentheses, so that's where we'll start. Remember, parentheses are like the VIP section of the math world – they get priority access!

Step 1: Tackling the Parentheses

Inside the parentheses, we have (-18-3). This is a simple subtraction, but be careful with those negative signs! Subtracting a positive number is like moving further to the left on the number line, so subtracting 3 from -18 will result in -21. So, (-18 - 3) = -21. We've successfully conquered the parentheses! It's like defusing the first part of a math bomb – we're making progress!

Understanding the role of parentheses is crucial in solving mathematical expressions accurately. Parentheses act as grouping symbols, telling us to perform the operations inside them before anything else. This ensures that certain parts of an expression are treated as a single unit, preventing miscalculations. Without parentheses, the order of operations might lead us to perform calculations in the wrong sequence, resulting in an incorrect answer. Think of parentheses as a way to create mini-problems within a larger problem, and we need to solve these mini-problems first.

Step 2: Multiplication

With the parentheses out of the way, we move on to the next operation according to PEMDAS: multiplication. We have -21 x 7. Multiplying a negative number by a positive number always gives us a negative result. So, we need to figure out what 21 multiplied by 7 is. If you're comfortable with your multiplication tables, you might already know that 21 x 7 = 147. If not, no worries! You can break it down: 20 x 7 = 140, and 1 x 7 = 7, so 140 + 7 = 147. Since we're multiplying a negative number, the result is -147. This step is like building the foundation of our solution – the stronger the foundation, the more stable the result!

Multiplication plays a vital role in mathematics, serving as a shorthand for repeated addition and forming the basis for many other operations. In this problem, multiplying -21 by 7 helps us determine the scaled value of the expression within the parentheses. Understanding multiplication is essential for solving a wide range of mathematical problems, from simple arithmetic to complex algebraic equations. It's like the engine that drives many calculations, so mastering multiplication is key to mathematical fluency. Without a solid grasp of multiplication, navigating more advanced concepts can become challenging.

Step 3: Addition

Finally, we reach the last operation: addition. We have -147 + (-23). Adding a negative number is the same as subtracting its positive counterpart. So, this is like saying -147 - 23. Think of it as starting at -147 on the number line and moving 23 steps further to the left. This will take us to -170. Therefore, the final answer is -170!

Addition, along with subtraction, forms the bedrock of arithmetic, allowing us to combine quantities and determine their total value. In this problem, adding -23 to -147 helps us reach the final solution by accounting for all the negative values in the expression. Understanding addition is not only crucial for solving mathematical problems but also for everyday tasks like managing finances, measuring ingredients while cooking, and calculating distances. It's like the glue that holds numbers together, enabling us to make sense of the world around us quantitatively. A firm understanding of addition paves the way for tackling more complex mathematical operations and concepts.

The Final Answer: -170

And there you have it! We've successfully navigated the mathematical maze and arrived at our final answer: -170. We started with a seemingly complicated expression, but by breaking it down step by step and following the order of operations, we made it manageable. Remember, math is like a puzzle – each step is a piece that fits into the bigger picture.

Key Takeaways

• Always remember PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.
• Tackle the parentheses first.
• Pay close attention to negative signs.
• Break down the problem into smaller, more manageable steps.

Practice Makes Perfect

The best way to master these skills is through practice. Try solving similar problems on your own, and don't be afraid to make mistakes. Mistakes are just opportunities to learn and improve. Think of each problem as a mini-challenge, and the more challenges you overcome, the stronger your math muscles will become.

Further Exploration

If you're feeling adventurous, try exploring more complex expressions with exponents and multiple sets of parentheses. You can also look into online resources and textbooks for additional practice problems and explanations. The world of math is vast and fascinating, and there's always something new to discover. So, keep exploring, keep practicing, and keep having fun with math!

So, the next time you encounter a math problem like (-18-3) x 7+(-23), remember this guide. You've got the tools and the knowledge to conquer it! Keep practicing, and you'll become a math whiz in no time. Remember, math isn't just about numbers; it's about problem-solving, logical thinking, and building a strong foundation for future learning. Keep up the great work, guys!