Solving 22 * (35 - 5) + 63 ÷ 7: A Step-by-Step Guide

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Hey guys! Math problems can sometimes look intimidating, right? But don't worry, we're going to break down this seemingly complex expression: 22 * (35 - 5) + 63 ÷ 7 step-by-step. We'll use the order of operations, also known as PEMDAS/BODMAS, to make sure we get to the correct answer. Trust me, it's easier than it looks, and by the end, you'll be a pro at tackling similar problems!

Understanding the Order of Operations (PEMDAS/BODMAS)

Before we dive into the calculation, it's crucial to understand the order of operations. This is the golden rule that dictates the sequence in which we perform mathematical operations. Think of it as a recipe – you need to follow the steps in the right order to get the delicious result! The acronyms PEMDAS and BODMAS are handy mnemonics to remember this order:

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

So, basically, we first deal with anything inside parentheses or brackets, then exponents or orders (like squares and cubes), followed by multiplication and division (working from left to right), and finally addition and subtraction (again, from left to right). Keeping this order in mind will prevent us from making common mistakes and ensure we arrive at the correct solution. Let's keep this order in our mind as we tackle the problem at hand. Ignoring this order is like trying to bake a cake by putting it in the oven before mixing the ingredients – you'll end up with a mess!

Step 1: Tackling the Parentheses

Our expression begins with a set of parentheses: (35 - 5). According to PEMDAS/BODMAS, this is the first thing we need to address. It's like clearing the first hurdle in a race – we need to conquer it to move forward. So, let's do the subtraction:

35 - 5 = 30

Now, we can substitute this result back into our original expression, which now looks like this: 22 * 30 + 63 ÷ 7. See? It's already looking less intimidating! We've successfully simplified the expression by taking care of the parentheses first. This step is super important because if we ignored the parentheses and did something else first, we'd end up with the wrong answer. Think of it as laying the foundation of a building – if the foundation is weak, the whole structure will be unstable. So, always remember to prioritize those parentheses!

Step 2: Multiplication and Division - The Dynamic Duo

Next up, we have multiplication and division. Remember, we perform these operations from left to right, just like reading a sentence. It's like following a road – we take the turns in the order they appear. So, let's start with the multiplication: 22 * 30. This part is all about quick arithmetic. Remember the basics, guys!

22 * 30 = 660

Great! Now, our expression looks even simpler: 660 + 63 ÷ 7. We've knocked out the multiplication, and now it's time to tackle the division. Next in line is 63 ÷ 7. This is where our times tables come in handy. Do you remember what number, when multiplied by 7, gives you 63? That's right, it's 9!

63 ÷ 7 = 9

Now, our expression is streamlined to a much more manageable form: 660 + 9. We've successfully navigated the multiplication and division steps, and we're on the home stretch! Remember, performing these operations in the correct order is essential. If we had jumped the gun and added 660 and 63 before dividing, we would have ended up with a completely different (and incorrect) result. So, stay focused, and keep following the PEMDAS/BODMAS road!

Step 3: Addition - The Grand Finale

Finally, we arrive at the last operation: addition. Our expression is now beautifully simplified to 660 + 9. This is the final step, the cherry on top, the last piece of the puzzle. Let's add these two numbers together:

660 + 9 = 669

And there we have it! The solution to our mathematical expression 22 * (35 - 5) + 63 ÷ 7 is 669. We've conquered the problem by methodically following the order of operations and breaking it down into smaller, manageable steps. This final addition is like the last brushstroke on a painting – it completes the masterpiece. We've taken a complex-looking expression and transformed it into a single, clear answer. Give yourselves a pat on the back – you've earned it!

Wrapping Up: The Thrill of the Solve

So, guys, we've successfully solved the expression 22 * (35 - 5) + 63 ÷ 7. Remember, the key is to take it one step at a time, follow the order of operations, and don't be afraid to break down the problem into smaller chunks. Math can be fun, especially when you approach it with a clear strategy. Understanding PEMDAS/BODMAS is like having a superpower in the math world – it allows you to tackle even the most daunting problems with confidence.

By understanding and applying the order of operations, we were able to navigate through parentheses, multiplication, division, and finally addition, to arrive at the correct answer: 669. This process not only gives us the solution but also reinforces the importance of structured problem-solving in mathematics. Keep practicing, and you'll become even more proficient at solving these kinds of expressions. And remember, every problem you solve is a step forward in your math journey!

Now you can confidently tackle similar mathematical expressions. Keep practicing, and you'll become a math whiz in no time! Remember, math isn't about memorizing formulas; it's about understanding the process and applying it logically. So, keep exploring, keep questioning, and keep solving!