Math Made Easy: Solving Equations Step-by-Step

by NGADEMIN 47 views
Iklan Headers

Understanding the Math Problem: 113+(25) -(-26) and Beyond!

Hey guys! Let's dive into this math problem: 113 + (25 - (-26)) * (-8) / 12. Sounds a bit intimidating, right? Don't worry, we'll break it down step by step, making it super easy to understand. We'll not only solve the original problem, but also explore the order of operations and how to tackle similar problems with confidence. This is all about making math fun and less scary. Ready? Let's get started!

Decoding the Original Problem: A Step-by-Step Guide

First things first, let's understand the components of the equation. We've got addition, subtraction, multiplication, and division – a classic mix! Remember the order of operations, often remembered by the acronym PEMDAS or BODMAS:

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

Following PEMDAS, we start with the parentheses. Inside the parentheses, we have 25 - (-26). Subtracting a negative number is the same as adding its positive counterpart. So, 25 - (-26) becomes 25 + 26, which equals 51. Now our equation simplifies to: 113 + 51 * (-8) / 12. Cool, huh? This seemingly complex problem is already becoming easier. Let's keep going!

Next up, we'll tackle the multiplication and division, working from left to right. We have 51 * (-8). Multiplying a positive number by a negative number results in a negative number. So, 51 * (-8) = -408. Our equation is now: 113 + (-408) / 12. Now, let's perform the division: -408 / 12 = -34. Our equation is getting simpler with each step. We are now at: 113 + (-34). Lastly, we perform the addition (or in this case, the addition of a negative number, which is the same as subtraction): 113 + (-34) = 113 - 34 = 79. And there you have it! The answer to the original math problem is 79. Not so bad, right?

Mastering the Order of Operations (PEMDAS/BODMAS)

The order of operations is the key to solving any math problem involving multiple operations. It's like a set of rules that ensures everyone arrives at the same correct answer. Imagine if we did the operations in a different order – we'd get a totally different result! That's why PEMDAS/BODMAS is so important. Let's go through some examples to make sure we really get it. Practice makes perfect!

Let's say we have 2 + 3 * 4. If we ignored the order of operations and just went left to right, we'd get 5 * 4 = 20. But that's wrong! Following PEMDAS, we multiply before we add. So, 3 * 4 = 12, and then 2 + 12 = 14. See the difference? Another example: (10 - 2) / 4 + 5. First, solve inside the parentheses: 10 - 2 = 8. Then, divide: 8 / 4 = 2. Finally, add: 2 + 5 = 7. Practicing with different types of problems will help you become more confident with the order of operations. If you're feeling stuck, just remember to follow PEMDAS/BODMAS, and you'll be fine.

More Math Problem Examples for Practice

Alright, let's test your skills with a few more problems. These are designed to reinforce your understanding of PEMDAS/BODMAS. Take your time, and remember to work step by step. Don't rush it; really understand each step. Then, we'll go through the answers together.

  1. 20 - 3 * (6 + 2) / 4
  2. 5 + 10 / 2 - 7
  3. (15 - 5) * 2 + 8 / 4
  4. 3 * (4 + 2) - 10 / 5

Now, try solving those problems on your own. Don't worry if you get stuck – it's all part of the learning process. The more you practice, the better you'll become. After you've given it a shot, we'll go over the solutions together to make sure we're all on the right track. Understanding and practicing different types of math problems is the best way to boost your confidence and get you feeling great about solving math problems! Ready? Go!

Solutions and Explanations for Practice Problems

Okay, guys, let's check our answers! Here are the solutions to the practice problems, along with detailed explanations. Let's see how you did.

  1. 20 - 3 * (6 + 2) / 4

    • First, solve inside the parentheses: 6 + 2 = 8.
    • Then, multiply: 3 * 8 = 24.
    • Next, divide: 24 / 4 = 6.
    • Finally, subtract: 20 - 6 = 14. The answer is 14.

  2. 5 + 10 / 2 - 7

    • First, divide: 10 / 2 = 5.
    • Then, add and subtract from left to right: 5 + 5 - 7 = 3. The answer is 3.

  3. (15 - 5) * 2 + 8 / 4

    • First, solve inside the parentheses: 15 - 5 = 10.
    • Then, multiply: 10 * 2 = 20.
    • Next, divide: 8 / 4 = 2.
    • Finally, add: 20 + 2 = 22. The answer is 22.

  4. 3 * (4 + 2) - 10 / 5

    • First, solve inside the parentheses: 4 + 2 = 6.
    • Then, multiply: 3 * 6 = 18.
    • Next, divide: 10 / 5 = 2.
    • Finally, subtract: 18 - 2 = 16. The answer is 16.

How did you do? Hopefully, you got them all correct! If not, no worries. The most important thing is that you now understand the correct way to solve these problems. Keep practicing, and you'll get even better. Math is really all about practice, so stick with it, and it will get easier with time. Don't give up!