Solving -10×(-2)-(-18): A Step-by-Step Guide

Hey guys! Today, we're going to break down how to solve the mathematical expression -10 × (-2) - (-18) step by step. Math can sometimes seem like a puzzle, but with the right approach and understanding of the rules, it becomes much easier. We'll also dive into the crucial sign rules you need to keep in mind while solving this type of problem. So, grab your pencils, and let's get started!

Understanding the Order of Operations

Before we jump into the expression itself, it's important to quickly recap the order of operations, often remembered by the acronym PEMDAS (or BODMAS in some regions). This is super important because following the correct order ensures we arrive at the right answer. PEMDAS stands for:

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

In our expression, -10 × (-2) - (-18), we have multiplication and subtraction. According to PEMDAS, we'll tackle the multiplication first. Keeping this order in mind will help us avoid any common pitfalls and get to the correct solution smoothly.

The Significance of Order of Operations in Complex Equations

The order of operations isn't just some arbitrary rule; it's the backbone of mathematical consistency. Without it, we'd have a chaotic mess where the same equation could yield multiple different answers depending on who's solving it. Imagine trying to build a house without a blueprint – that's what math without PEMDAS feels like! The order of operations provides a standardized approach, ensuring that mathematicians, students, and even computers across the globe can all solve the same problem and arrive at the same correct answer. This consistency is especially crucial in more complex equations involving multiple operations, parentheses, exponents, and more. By adhering to this order, we're not just crunching numbers; we're speaking a universal language that transcends borders and disciplines. So, next time you're faced with a lengthy equation, remember PEMDAS or BODMAS – your trusty guide to mathematical clarity!

PEMDAS in Real-World Applications

The principles of PEMDAS aren't just confined to the classroom or textbook; they pop up in all sorts of real-world scenarios, often without us even realizing it. Think about coding, for example. When programmers write code, they're essentially creating a set of instructions for the computer to follow. If the operations aren't executed in the correct order, the program could crash or produce unexpected results. Financial calculations are another prime example. Calculating compound interest, returns on investments, or even balancing your checkbook all require a precise order of operations. A small mistake in sequencing the calculations can lead to significant errors in the final figures. Even in everyday situations like cooking, following a recipe involves understanding the order of operations. Adding ingredients at the wrong time or skipping a crucial step can result in a culinary disaster. So, whether you're building software, managing your finances, or whipping up a delicious meal, the order of operations is your silent partner in ensuring accuracy and success. It's a fundamental skill that empowers us to approach problems logically and systematically, no matter the context.

Step-by-Step Solution

Now, let's solve -10 × (-2) - (-18) together, step by step.

Step 1: Multiplication

First, we multiply -10 by -2. Remember the sign rule: a negative number multiplied by a negative number results in a positive number. So:

-10 × (-2) = 20

Step 2: Rewrite the Expression

Now, we substitute the result back into the expression:

20 - (-18)

Step 3: Subtraction of a Negative Number

Subtracting a negative number is the same as adding its positive counterpart. Think of it like this: taking away a debt is the same as gaining money. So:

20 - (-18) = 20 + 18

Step 4: Addition

Finally, we add 20 and 18:

20 + 18 = 38

So, the solution to the expression -10 × (-2) - (-18) is 38. We made it! By following the order of operations and paying close attention to the sign rules, we've successfully navigated this mathematical puzzle. It's all about breaking it down into smaller, manageable steps and tackling each one with confidence. Keep practicing, and you'll become a math whiz in no time!

Common Mistakes to Avoid When Solving Similar Expressions

When tackling expressions like -10 × (-2) - (-18), there are a few common pitfalls that students often stumble into. One of the biggest mistakes is ignoring the order of operations, or PEMDAS. It's tempting to just go from left to right, but this can lead to incorrect results. Another frequent error involves mishandling negative signs. For instance, forgetting that subtracting a negative number is the same as adding its positive counterpart can throw off the entire calculation. Also, students sometimes struggle with the sign rules in multiplication and division, particularly when dealing with multiple negative numbers. It's crucial to remember that a negative times a negative is a positive, while a negative times a positive is a negative. To avoid these mistakes, always double-check your work, especially when it comes to signs. Practice regularly, break down complex expressions into smaller steps, and don't hesitate to use parentheses to clarify the order of operations. With a little diligence, you can dodge these common errors and boost your math confidence!

Sign Rules: A Quick Guide

Let's solidify our understanding of the sign rules. These rules are the backbone of arithmetic operations with positive and negative numbers.

• Multiplication and Division:

  • Negative × Negative = Positive
  • Positive × Positive = Positive
  • Negative × Positive = Negative
  • Positive × Negative = Negative

  The same rules apply to division.

• Addition and Subtraction:

  • When adding numbers with the same sign, add their absolute values and keep the sign.
  • When adding numbers with different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value.
  • Subtracting a negative number is the same as adding its positive counterpart.

Mastering these sign rules is key to solving mathematical expressions accurately. They might seem straightforward, but a small slip-up can change the entire outcome. So, make sure you have these rules down pat, and you'll be well-equipped to tackle any math problem that comes your way!

Real-Life Examples of Sign Rules in Action

Sign rules aren't just abstract mathematical concepts; they're constantly at play in our everyday lives, often without us even realizing it. Consider your bank account, for example. Deposits are positive numbers, adding to your balance, while withdrawals are negative numbers, subtracting from it. Understanding the sign rules helps you keep track of your finances, ensuring you don't accidentally overdraw your account. Temperature is another area where sign rules are crucial. Temperatures above zero are positive, while those below zero are negative. Knowing how to add and subtract negative temperatures is essential for weather forecasting, as well as for practical decisions like what to wear or whether to expect frost. Even in sports, sign rules play a role. In golf, scores above par are positive, while scores below par are negative. Calculating a golfer's total score involves adding and subtracting these positive and negative numbers. So, from managing your money to understanding the weather, sign rules are a fundamental tool for navigating the world around us. They provide a framework for representing and manipulating quantities that can be both positive and negative, making them an indispensable part of our daily lives.

Mnemonics and Tricks to Remember Sign Rules

Let's be honest, memorizing rules can sometimes feel like a chore. But fear not, there are some clever mnemonics and tricks to help you remember the sign rules without pulling your hair out! For multiplication and division, a simple rhyme can work wonders: