Fraction Of Salary Spent On Vacation: A Math Problem

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Hey guys! Let's break down this math problem together. Carla spent 75% of her salary on a vacation, and we need to figure out what fraction that percentage represents. This is a pretty common type of question, and once you understand the basics, it becomes super easy to solve. We'll go through the steps, explain the concepts, and make sure you get it! So, stick around and let's get started!

Understanding Percentages and Fractions

Before diving into the problem, let's quickly recap what percentages and fractions are. A percentage is a way of expressing a number as a fraction of 100. So, 75% simply means 75 out of 100. A fraction, on the other hand, represents a part of a whole. It's written as one number over another, like 1/2 or 3/4. The number on top (numerator) shows how many parts we have, and the number on the bottom (denominator) shows how many parts the whole is divided into.

Converting between percentages and fractions is a fundamental skill in math. To convert a percentage to a fraction, you simply write the percentage as a fraction with a denominator of 100. For example, 50% becomes 50/100. Then, you simplify the fraction to its lowest terms. This means finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by that number. Understanding this conversion is crucial for solving problems like the one we have with Carla's vacation spending. It allows us to express the same value in different forms, making it easier to work with depending on the context. So, with these basics in mind, let's tackle Carla's problem and find out what fraction of her salary she spent.

Converting 75% to a Fraction

Okay, so Carla spent 75% of her salary. To find out what fraction that is, we first write 75% as a fraction with a denominator of 100. That gives us 75/100. Now, we need to simplify this fraction. Both 75 and 100 are divisible by 25. If we divide both the numerator (75) and the denominator (100) by 25, we get 3/4. So, 75% is equal to the fraction 3/4. This means Carla spent 3/4 of her salary on her vacation. Isn't that neat how we can easily switch between percentages and fractions?

Simplifying fractions is a key skill, and it's all about finding common factors. In this case, recognizing that both 75 and 100 are divisible by 25 made the simplification straightforward. But what if you didn't immediately see that 25 was the greatest common divisor? Well, you could start by dividing both numbers by a smaller factor, like 5. That would give you 15/20. Then, you'd notice that 15 and 20 are also divisible by 5, and you'd divide again to get 3/4. The important thing is to keep simplifying until you can't divide any further. Whether you find the greatest common divisor right away or take it step by step, the goal is always to get the fraction in its simplest form. This not only makes the fraction easier to understand but also helps in comparing and performing other mathematical operations with it. So, practice simplifying fractions whenever you get the chance, and you'll become a pro in no time!

The Answer

So, the fraction of Carla's salary that she spent on her vacation is 3/4. Therefore, the correct answer is (B) 3/4.

Why the Other Options Are Incorrect

Let's quickly look at why the other options are wrong:

  • (A) 1/4: This would be 25% of her salary, not 75%.
  • (C) 4/3: This is greater than 1, which means more than 100% of her salary. Carla couldn't have spent more than her entire salary.
  • (D) 5/4: This is also greater than 1, representing more than 100% of her salary, which isn't possible.

Understanding why the incorrect options are wrong is just as important as knowing why the correct answer is right. It helps reinforce your understanding of the concepts and prevents you from making similar mistakes in the future. In this case, recognizing that 1/4 represents 25% immediately rules out option A. Similarly, knowing that a fraction greater than 1 represents more than 100% helps you eliminate options C and D. By analyzing the incorrect options, you deepen your comprehension and improve your problem-solving skills. So, always take the time to understand why an answer is wrong – it's a valuable learning opportunity!

Real-World Application

This kind of problem isn't just for school. It's something you might use in real life. For example, when budgeting for a trip or understanding discounts at the store. Let's say you see a sign that says "25% off." You can quickly convert that to 1/4 to figure out how much you're saving. Or, if you want to save 1/3 of your income, you know that's about 33.3%. These skills come in handy more often than you might think!

Understanding how to convert percentages to fractions and vice versa is a practical skill that extends far beyond the classroom. It's a tool that empowers you to make informed decisions in various real-life situations. Whether you're calculating discounts while shopping, figuring out tips at a restaurant, or managing your personal finances, the ability to work with percentages and fractions is invaluable. For instance, when comparing different loan offers, you might need to convert interest rates (percentages) into fractions to understand the true cost of borrowing. Similarly, when following a recipe, you might need to adjust ingredient quantities based on a fraction of the original recipe. By mastering these conversions, you become more confident and capable in navigating everyday financial and mathematical challenges. So, keep practicing and applying these skills, and you'll find yourself using them more and more in your daily life!

Practice Makes Perfect

To get even better at this, try some more practice problems. For example:

  • What fraction is 20%?
  • What percentage is 1/2?
  • Convert 60% to a fraction.

The more you practice, the easier it will become. Keep up the great work!

Keep practicing, and you'll become more comfortable and confident with these types of conversions. Try applying these concepts to different scenarios, like calculating discounts while shopping or figuring out proportions in a recipe. The more you use these skills, the more natural they'll become. And remember, if you ever get stuck, don't hesitate to review the basics or ask for help. Math can be challenging, but it's also incredibly rewarding. So, keep pushing yourself, stay curious, and never stop learning. With consistent effort and the right resources, you can conquer any math problem that comes your way. So, go out there and practice, and watch your skills grow!

Conclusion

So, Carla spent 3/4 of her salary on vacation. We figured this out by converting the percentage (75%) to a fraction. Remember, percentages and fractions are just different ways of showing the same thing. Keep practicing, and you'll become a math whiz in no time! Keep rocking, guys!