Solving Math Expressions: A Step-by-Step Guide

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Solving Math Expressions: A Step-by-Step Guide

Hey math enthusiasts! Let's dive into some cool math problems. Today, we're going to break down how to solve a bunch of expressions. We'll be tackling things like addition, subtraction, multiplication, and division, with a little help from some negative numbers. Ready to sharpen those math skills? Let's get started!

Diving into the Problems: A Quick Overview

Alright, guys, before we jump into the nitty-gritty, let's take a look at the expressions we'll be working with. We've got a variety of problems that will help us practice different operations and get comfortable with negative numbers. This is where we put our knowledge to the test, and don't worry if it seems a little tricky at first. We'll go through each step together. The key is to take it slow, understand each part, and practice, practice, practice! Each expression offers a unique challenge, requiring us to apply different rules and concepts. As we solve these, we'll reinforce our understanding of order of operations, integer arithmetic, and fraction manipulation. By the end of this guide, you should feel more confident in tackling similar problems on your own.

Now, here are the expressions we'll be solving:

  1. 10 - (-2)
  2. 8½ * (-7)
  3. 63 / (-2)
  4. 126 / 2
  5. 53 / (-711)
  6. 7 11 / (-9)

We will approach these expressions one by one, providing a detailed explanation of each step. We will break down each problem into smaller, manageable parts. We'll explain the reasoning behind each step, ensuring you understand not just how to solve the problem, but also why the solution works. Let’s get our math hats on and get started. Trust me; it's easier than it looks. Understanding the steps will make you feel like a math whiz in no time!

Solving Each Expression Step by Step

Expression 1: 10 - (-2)

Let’s start with the first one: 10 - (-2). This problem involves subtraction, and it throws in a little twist with negative numbers. When you subtract a negative number, it's the same as adding a positive number. So, 10 - (-2) becomes 10 + 2. The concept of subtracting a negative number can be a little confusing, but remember that the two negative signs cancel each other out, turning the subtraction into addition. That makes this problem pretty straightforward. Adding 10 and 2, we get 12. So, the solution is:

  1. 10 - (-2) = 10 + 2
  2. 10 + 2 = 12

So, the answer to our first expression is 12. Easy peasy, right?

Expression 2: 8½ * (-7)

Next up, we have 8½ * (-7). This one involves multiplication, and we have a mixed number and a negative number to deal with. First, let's convert the mixed number 8½ into an improper fraction. To do this, we multiply the whole number (8) by the denominator (2) and add the numerator (1). This gives us 16 + 1 = 17. So, 8½ becomes 17/2. Now our expression is (17/2) * (-7). When multiplying a positive number by a negative number, the result is always negative. Multiply the numerator of the fraction (17) by -7 and then divide by the denominator (2). This is (17 * -7) / 2 = -119/2. To express this as a mixed number, we divide -119 by 2, which gives us -59 with a remainder of -1, so this becomes -59½. Therefore, the solution is:

  1. Convert 8½ to an improper fraction: 8½ = 17/2
  2. Multiply: (17/2) * (-7) = -119/2
  3. Convert to mixed number: -119/2 = -59½

So, the answer is -59½.

Expression 3: 63 / (-2)

Let’s tackle 63 / (-2). Here, we're dividing a positive number by a negative number. This means our answer will be negative. When dividing, you can think of it as splitting a quantity into equal parts. Dividing 63 by -2 results in -31.5. This can also be expressed as -31½. So, the solution is:

  1. Divide 63 by -2: 63 / -2 = -31.5

Thus, the result is -31.5 or -31½.

Expression 4: 126 / 2

Now, let's move on to 126 / 2. This is a straightforward division problem where we're dividing a positive number by another positive number. Divide 126 by 2. When you divide 126 by 2, you get 63. This is a basic division problem where we're simply splitting a quantity into two equal parts. So the solution is:

  1. Divide 126 by 2: 126 / 2 = 63

The answer to this expression is 63. Easy, right?

Expression 5: 53 / (-711)

Next, let's look at 53 / (-711). Here, we're dividing a positive number (53) by a negative number (-711). Because we're dividing by a negative number, our answer will be negative. The result of 53 divided by -711 is approximately -0.0745, which can be expressed as a fraction. This is where a calculator might come in handy to ensure accuracy, but understanding the concept is key! So the solution is:

  1. Divide 53 by -711: 53 / -711 ≈ -0.0745

The answer to this expression is approximately -0.0745. or -53/711.

Expression 6: 7 11 / (-9)

Lastly, we have 7 11 / (-9). This involves a mixed number and division by a negative number. First, let's convert the mixed number 7 11 to an improper fraction. To convert this mixed number, multiply the whole number (7) by the denominator (11) and add the numerator (11). This gives us (7 * 11) + 11 = 77 + 11 = 88. So 7 11 = 88/11. The expression now becomes 88/11 / (-9). Now we divide the fraction by -9. Dividing by a number is the same as multiplying by its reciprocal. So we multiply the fraction by -1/9. Which equals (88/11) * (-1/9) = -88/99. The fraction can be simplified to -8/9. The solution is:

  1. Convert 7 11 to an improper fraction: 7 11 = 88/11
  2. Divide by -9: (88/11) / (-9) = (88/11) * (-1/9) = -88/99
  3. Simplify the fraction: -88/99 = -8/9

Therefore, the answer is -8/9.

Conclusion: You've Got This!

Alright, guys, you've successfully worked through all the expressions! We've covered a variety of operations and tackled different types of numbers, including fractions, mixed numbers, and negative numbers. Remember, the key to mastering math is practice. The more you work through problems, the more confident you'll become. So, keep practicing, keep learning, and don't be afraid to ask for help when you need it. You've totally got this! Feel free to revisit these examples and try similar problems on your own. Keep up the awesome work!