Solve 95 / (1/5) + 35: Step-by-Step Guide

by Alex Braham 42 views

Hey everyone! Today, we're diving into a math problem that might seem a little intimidating at first glance: 95 divided by one-fifth, plus 35. Don't worry, though; we're going to break it down step by step, so you'll understand it perfectly. This isn't just about getting the right answer; it's about understanding the process and the concepts behind it. By the end of this guide, you'll be able to tackle similar problems with confidence. So, let's get started!

Breaking Down the Problem: Order of Operations

When we see a math problem like this, the first thing we need to remember is the order of operations. You might have heard of the acronym PEMDAS or BODMAS. They both tell us the same thing: the order in which we need to solve the different parts of a mathematical expression. In case you forgot, here's what those acronyms stand for:

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

In our problem, 95 / (1/5) + 35, there are no parentheses or exponents. So, according to PEMDAS/BODMAS, our first step is to handle the division part of the equation: 95 divided by one-fifth. This is really crucial, since you must get this right to proceed.

Performing the Division

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is simply the fraction flipped over. In this case, the reciprocal of 1/5 is 5/1, which is just 5. So, instead of dividing 95 by 1/5, we can multiply 95 by 5. The basic mathematical steps are as follows:

  • 95 / (1/5) = 95 * 5
  • 95 * 5 = 475

See? It's not as scary as it looked at first, right? We've successfully handled the division part and got 475. This is a very important part, so you should understand the basics of this process. It is important to remember what order of operations mean and how to make the calculations correctly. Now, we are ready to move on the next step!

Adding the Final Value

Now that we've completed the division step, we're left with a simple addition problem. Remember, we had 95 / (1/5) + 35. We've figured out that 95 / (1/5) equals 475. So, our equation now looks like this: 475 + 35. Adding these two numbers together is straightforward. If you're doing this by hand, you'll line up the numbers by place value (ones, tens, hundreds) and add them up. Let’s make the calculations:

  • 475
    • 35
  • 510

So, 475 + 35 = 510. The result is just 510. Easy, right? Remember to double-check your work, but it should be alright. Always make the effort to understand the process. It's the most important thing. Now we are good to go, we have the answer.

The Final Answer

Alright, guys! We've done it. We've successfully solved the equation 95 / (1/5) + 35. After following the order of operations, we found that:

95 / (1/5) + 35 = 510

So, the answer is 510. This is the final result of our work. Congratulations! You've not only solved the problem, but you've also reinforced your understanding of the order of operations and how to work with fractions. Remember that practice is key, so don't be afraid to try similar problems on your own. Keep practicing, and you'll become a math whiz in no time. Always have in mind the different rules. Always remember what PEMDAS or BODMAS stand for. You will achieve the best results by applying them.

Tips for Similar Problems

  • Always follow the order of operations. This is the golden rule!
  • Convert division by fractions into multiplication by the reciprocal. This makes the process much easier.
  • Double-check your work. Mistakes happen, so it's always good to review your steps.
  • Practice, practice, practice! The more you practice, the more comfortable you'll become with these types of problems.

Conclusion

So there you have it! We've successfully navigated the math problem 95 / (1/5) + 35, breaking it down step by step and arriving at the correct answer of 510. By understanding the order of operations, the concept of reciprocals, and simple addition, we've transformed what might have seemed like a complex equation into a manageable task. Remember, math isn't about memorizing formulas; it's about understanding the logic behind them. I hope this guide helps you feel more confident about solving similar math problems in the future. Keep practicing, stay curious, and you'll find that math can actually be pretty fun. Don't worry, guys, you're doing great!

FAQs

Q: What is the order of operations?

A: The order of operations (PEMDAS/BODMAS) tells us the sequence in which we solve a mathematical expression. It's Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Q: How do I divide by a fraction?

A: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is found by flipping the fraction over (e.g., the reciprocal of 1/2 is 2/1).

Q: What if there are multiple sets of parentheses?

A: If there are nested parentheses (parentheses within parentheses), you solve the innermost set of parentheses first and work your way outwards.

Q: How can I improve my math skills?

A: Practice regularly, work through examples, and don't be afraid to ask for help when you need it. Online resources and textbooks can also be very helpful.

Q: Why is understanding the order of operations important?

A: The order of operations ensures that everyone solves mathematical expressions in the same way, leading to consistent and accurate results. Without it, you could get different answers for the same problem.

Q: What if I forget the order of operations?

A: If you forget the order of operations, you can use the acronyms PEMDAS or BODMAS to help you remember the correct sequence.