Solving 6 - 3(4-6) + (10:5) 28:7: A Step-by-Step Guide

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Solving the Math Problem: 6 - 3(4-6) + (10:5) 28:7

Hey guys! Let's break down this math problem together. It looks a bit intimidating at first, but don't worry, we'll take it one step at a time. This problem involves a mix of operations, so we need to remember our order of operations – PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Let’s dive in and make math a little less scary, okay?

Understanding the Order of Operations (PEMDAS/BODMAS)

Before we jump into solving the problem, it's super important to understand the order of operations. You might have heard of PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). They both mean the same thing – it’s just a handy way to remember the sequence in which we should tackle mathematical operations. Think of it as the golden rule of math!

  • Parentheses/Brackets: Always start by simplifying anything inside parentheses or brackets. This is your first priority.
  • Exponents/Orders: Next up are exponents or orders (like squares and cubes). If you see any, calculate those next.
  • Multiplication and Division: Multiplication and division come next. Remember, you perform these operations from left to right.
  • Addition and Subtraction: Finally, we handle addition and subtraction, also from left to right.

By sticking to this order, we ensure that we solve the problem correctly and consistently. So, keep PEMDAS/BODMAS in mind as we move forward. It’s our trusty guide in the world of mathematical operations!

Step-by-Step Solution

Now, let's apply PEMDAS to our problem: 6 - 3(4-6) + (10:5) 28:7. We will go through each step meticulously so you can follow along easily. Remember, math is like building blocks – each step builds on the previous one, leading us to the correct answer. So, let's put on our math hats and get started!

1. Parentheses

First, we tackle the parentheses: (4 - 6) and (10 : 5).

  • (4 - 6) = -2. This is straightforward subtraction within the parentheses. When you subtract a larger number from a smaller one, you end up with a negative result. Think of it like starting at 4 and moving 6 steps backward on a number line – you'll land at -2.
  • (10 : 5) = 2. This is a simple division. 10 divided by 5 equals 2. It's like splitting 10 items into 5 equal groups – each group will have 2 items.

So, our equation now looks like this: 6 - 3(-2) + 2 * 28 : 7. We've successfully simplified the expressions within the parentheses, and we’re one step closer to the solution. Next up, we'll deal with multiplication and division.

2. Multiplication and Division

Next, we perform multiplication and division from left to right. This is a crucial step, so let's take our time and ensure we get it right.

  • -3(-2) = 6. Here, we're multiplying two negative numbers. Remember, a negative times a negative gives you a positive. So, -3 multiplied by -2 equals positive 6.
  • 2 * 28 = 56. This is simple multiplication. 2 multiplied by 28 equals 56.
  • 56 : 7 = 8. Now we divide. 56 divided by 7 equals 8. Think of it as splitting 56 into 7 equal parts – each part would be 8.

After these operations, our equation looks like this: 6 + 6 + 8. We’ve handled all the multiplication and division, and now we’re left with a simple addition problem. It's getting easier, right? Let’s move on to the final step.

3. Addition and Subtraction

Finally, we perform addition and subtraction from left to right. In our simplified equation, 6 + 6 + 8, we only have addition operations left, which makes it even simpler!

  • 6 + 6 = 12. We start by adding the first two numbers.
  • 12 + 8 = 20. Then, we add the result to the last number.

So, after performing all the additions, we arrive at our final answer: 20. We’ve successfully navigated through the problem step by step, and we’ve reached the solution. Give yourself a pat on the back – you’ve earned it!

Final Answer

Therefore, the result of the operation 6 - 3(4-6) + (10:5) 28:7 is 20. Wasn't so bad when we broke it down, right? Remember, the key to solving complex problems is to take it one step at a time and follow the correct order of operations. Math can be fun when you approach it methodically!

Tips for Solving Similar Problems

Now that we’ve cracked this problem, let’s talk about some tips that can help you tackle similar mathematical challenges in the future. These strategies are like having extra tools in your math toolkit. The more you practice and apply them, the more confident you’ll become in your problem-solving abilities. So, let’s dive into some helpful tips and tricks!

1. Always Follow PEMDAS/BODMAS

This is the golden rule! Always adhere to the order of operations (PEMDAS/BODMAS). It ensures you solve the problem in the correct sequence. This means starting with parentheses, then exponents, followed by multiplication and division (from left to right), and finally, addition and subtraction (also from left to right). Think of PEMDAS/BODMAS as your roadmap for solving mathematical expressions.

2. Break Down the Problem

Complex problems can seem less daunting when you break them down into smaller, manageable steps. Identify the different operations and tackle them one at a time. This not only makes the problem easier to handle but also reduces the chances of making errors. It’s like eating an elephant – you do it one bite at a time!

3. Show Your Work

It's tempting to skip writing down each step, but showing your work is super helpful. It allows you to track your progress, identify mistakes more easily, and makes it simpler to review your solution later. Plus, it’s a great habit to develop for more complex math problems you’ll encounter in the future. Think of it as creating a trail that you can follow back if you get lost.

4. Double-Check Your Calculations

Always take a moment to double-check your calculations, especially in exams or important assignments. Simple arithmetic errors can sometimes lead to incorrect answers, even if you understand the underlying concepts. A quick review can save you from losing valuable points. It’s like proofreading a document before you submit it – always a good idea!

5. Practice Regularly

The more you practice, the better you'll become at solving math problems. Regular practice helps you become more comfortable with different types of questions and reinforces the concepts you've learned. Try solving a variety of problems to challenge yourself and improve your skills. Think of it as exercising a muscle – the more you use it, the stronger it gets.

6. Use Online Resources

There are tons of fantastic online resources available that can help you with math. Websites like Khan Academy, YouTube channels dedicated to math tutorials, and various math apps can provide additional explanations, examples, and practice problems. Don’t hesitate to use these resources to supplement your learning. They’re like having a virtual tutor available 24/7!

7. Seek Help When Needed

If you’re struggling with a particular concept or problem, don’t hesitate to ask for help. Talk to your teacher, classmates, or a tutor. Sometimes, a different explanation or perspective can make all the difference. Remember, asking for help is a sign of strength, not weakness. It shows that you’re proactive about your learning.

By incorporating these tips into your problem-solving approach, you’ll be well-equipped to handle a wide range of math problems with confidence and ease. So, keep practicing, stay curious, and remember that every challenge is an opportunity to learn and grow!

Conclusion

So, there you have it! We’ve successfully solved the problem 6 - 3(4-6) + (10:5) 28:7, and we’ve also armed ourselves with some handy tips for tackling similar math challenges. Remember, the world of mathematics might seem complex at times, but with a systematic approach and a bit of practice, you can conquer any equation that comes your way. Keep that PEMDAS/BODMAS order in mind, break down problems into smaller steps, and don't be afraid to ask for help when you need it. Math is like a puzzle – challenging, but incredibly rewarding when you find the solution. Keep exploring, keep learning, and most importantly, keep enjoying the journey of mathematical discovery!