Let's break down how to solve the math problem "95 divided by one fifth plus 35". It might look a little tricky at first, but don't worry, we'll go through it step by step to make it super clear. Understanding the order of operations is key here, so we'll use the PEMDAS/BODMAS method to get the right answer. Ready? Let's dive in!

Understanding the Order of Operations

Alright, before we jump into the problem, let's quickly chat about the order of operations. You might have heard of PEMDAS or BODMAS. It’s just a fancy way of saying what order we need to do things in math to get the right answer. PEMDAS stands for:

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

BODMAS is pretty much the same thing but uses different words:

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

Basically, both tell us to do the stuff inside parentheses first, then exponents (or orders), then multiplication and division (from left to right), and finally addition and subtraction (again, from left to right). Keeping this order in mind is super important; otherwise, we might end up with the wrong answer. Think of it like following a recipe – you need to add the ingredients in the right order, or the cake might not turn out so great!

Understanding PEMDAS/BODMAS is like having a secret weapon in math. It helps you tackle even the trickiest problems with confidence. For instance, if you have an equation like 2 + 3 * 4, you wouldn't just add 2 and 3 first. Instead, you'd multiply 3 and 4 to get 12, and then add 2, resulting in 14. If you did it the other way, you'd get 20, which is totally wrong! So, always remember to follow the order of operations to keep your calculations accurate and avoid common mistakes. This is especially important in more complex problems where multiple operations are involved. So, let's keep PEMDAS/BODMAS in our back pocket as we move forward and solve our problem step by step. This ensures that we're not just crunching numbers, but we're doing it in the correct, mathematically sound way!

Step-by-Step Solution: 95 Divided by 1/5 Plus 35

Okay, let's get to the main event: solving "95 divided by one fifth plus 35." Here’s how we'll break it down:

Step 1: Rewrite the Division

First, we need to understand what “95 divided by one fifth” means. Dividing by a fraction is the same as multiplying by its reciprocal. So, dividing by 1/5 is the same as multiplying by 5/1 (which is just 5). This makes our problem much easier to handle. Instead of dealing with fractions right away, we can convert the division into a multiplication problem. This simple switch can save us a lot of headaches and potential errors. When you see division by a fraction, remember this trick: flip the fraction and multiply! It's a handy shortcut that simplifies the calculation and makes the problem more approachable. This step is crucial because it sets the stage for the rest of the solution. By correctly converting the division into multiplication, we ensure that our subsequent calculations are accurate and lead us to the right answer. So, let's keep this tip in mind for future problems as well! Understanding this conversion is key to mastering fraction-related math.

Step 2: Perform the Multiplication

Now we rewrite the problem as 95 * 5 + 35. According to PEMDAS/BODMAS, we need to do the multiplication before we do the addition. So, let’s multiply 95 by 5.

95 * 5 = 475

So, now we know that 95 divided by one fifth (or 95 multiplied by 5) equals 475. This step is straightforward but super important. Getting the multiplication right ensures that the rest of our calculation will be accurate. Multiplication is a fundamental operation in math, and mastering it is essential for solving more complex problems. Take your time to double-check your multiplication to avoid any small errors that could throw off the entire solution. Remember, even a tiny mistake in multiplication can lead to a completely different final answer. Accuracy is key, so let's make sure we've got this step down pat before we move on to the addition. With the multiplication correctly done, we're one step closer to cracking this problem! The result, 475, now becomes a key component in our final calculation.

Step 3: Perform the Addition

Now we have 475 + 35. This is the last step! Let's add these two numbers together:

475 + 35 = 510

So, 95 divided by one fifth plus 35 equals 510. That's it! We've solved the problem step by step, following the order of operations to get the correct answer. Addition is the final piece of the puzzle, and it brings us to the ultimate solution. Double-check your addition to ensure that you haven't made any minor errors. Accuracy is crucial at this stage, as it's the last step before arriving at the final answer. Once you're confident in your addition, you can proudly say that you've successfully solved the problem. Remember, each step in the process is important, and by following the correct order of operations, you can tackle any mathematical challenge with confidence. So, congratulations on reaching the end and arriving at the correct solution: 510!

Final Answer

So, after following all the steps carefully, we've found that:

95 ÷ (1/5) + 35 = 510

Therefore, the final answer is 510.

Common Mistakes to Avoid

When tackling problems like these, it's easy to slip up if you're not careful. Here are a few common mistakes to watch out for:

1. Ignoring Order of Operations: This is the biggest pitfall. If you don't follow PEMDAS/BODMAS, you'll likely get the wrong answer. Always remember to do multiplication and division before addition and subtraction.
2. Incorrectly Inverting the Fraction: When dividing by a fraction, make sure you flip it correctly to multiply. Forgetting to do this, or doing it wrong, will lead to an incorrect result.
3. Simple Arithmetic Errors: Sometimes, the mistake isn't in the concept but in the basic math. Double-check your multiplication and addition to avoid these little errors.
4. Rushing Through the Problem: Take your time and go step by step. Rushing can lead to careless mistakes that are easily avoidable.

Avoiding these mistakes can save you a lot of frustration and ensure that you get the correct answer every time. Always double-check your work, especially if the problem seems straightforward. A little bit of caution can go a long way in math!

Practice Problems

Want to make sure you've really got this down? Here are a few practice problems you can try. Remember to follow the order of operations and double-check your work!

1. 120 ÷ (1/4) + 20
2. 75 + 50 ÷ (1/2)
3. 100 ÷ (1/5) - 45

Work through these problems step by step, and you'll become a pro at solving these types of equations in no time. Practice makes perfect, so the more you do, the more comfortable you'll become with these concepts.

Conclusion

So, there you have it! We've successfully solved the problem "95 divided by one fifth plus 35" by breaking it down into simple, manageable steps. Remember the importance of the order of operations (PEMDAS/BODMAS) and how to handle division by fractions. With these tools in your math kit, you'll be able to tackle all sorts of similar problems with confidence. Keep practicing, and you'll become a math whiz in no time! Great job on making it to the end, and keep up the fantastic work!