Fractions: Find The Non-Equivalent Of 0.75

Hey guys! Let's dive into a fun fraction problem today. Our mission, should we choose to accept it, is to figure out which fraction isn't the same as 0.75. We've got four options: A. $\frac{15}{20}$, B. $\frac{9}{12}$, C. $\frac{6}{9}$, and D. $\frac{3}{4}$. So, grab your metaphorical magnifying glasses, and let's get started!

Understanding Equivalent Fractions

Before we jump into solving this, let's quickly recap what equivalent fractions are all about. Equivalent fractions are fractions that might look different, but they actually represent the same value. Think of it like this: $\frac{1}{2}$ is the same as $\frac{2}{4}$, $\frac{3}{6}$, $\frac{4}{8}$, and so on. They're all just different ways of saying the same thing. To find equivalent fractions, you can multiply or divide both the numerator (the top number) and the denominator (the bottom number) by the same non-zero number. This keeps the ratio the same, which means the value of the fraction doesn't change. For instance, if you have $\frac{1}{2}$ and you multiply both the top and bottom by 2, you get $\frac{2}{4}$, which is equivalent. If you multiply both by 3, you get $\frac{3}{6}$, still equivalent. The key is that you're scaling both parts of the fraction proportionally. Understanding this concept is crucial because it allows us to compare fractions that look different at first glance. Now, let's bring this knowledge back to our problem and see which of the given fractions doesn't fit the 0.75 bill. We'll convert each fraction to its simplest form or decimal equivalent to make comparisons easier. It's all about finding which one stands out as the odd one out, the one that just doesn't belong in our 0.75 club.

Converting Fractions to Decimals

Now, let's convert 0.75 into a fraction to make it easier to compare. 0.75 is the same as $\frac{75}{100}$. If we simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (which is 25), we get $\frac{3}{4}$. So, we're looking for the fraction that isn't equivalent to $\frac{3}{4}$. Another handy trick is to convert each fraction into a decimal. This often makes it super clear which ones are equivalent. To convert a fraction to a decimal, you simply divide the numerator by the denominator. For example, to convert $\frac{1}{2}$ to a decimal, you divide 1 by 2, which gives you 0.5. Similarly, to convert $\frac{1}{4}$ to a decimal, you divide 1 by 4, resulting in 0.25. Knowing how to switch between fractions and decimals gives you a versatile toolkit for solving problems. You can choose the format that makes the comparison easiest for you. In our case, since we're given 0.75, converting the fractions to decimals will likely be the most straightforward approach. Keep this conversion skill in your back pocket; it's a lifesaver in many math situations!

Evaluating Option A: $\frac{15}{20}$

Let's start with option A: $\frac{15}{20}$. To determine if it's equivalent to 0.75, we can simplify the fraction or convert it to a decimal. If we simplify $\frac{15}{20}$, we can divide both the numerator and the denominator by their greatest common divisor, which is 5. Doing this, we get $\frac{15 \div 5}{20 \div 5} = \frac{3}{4}$. Aha! So, $\frac{15}{20}$ simplifies to $\frac{3}{4}$, which we already know is equal to 0.75. Alternatively, we could convert $\frac{15}{20}$ to a decimal by dividing 15 by 20. Doing this, we get 0.75. Either way, we arrive at the same conclusion: $\frac{15}{20}$ is indeed equivalent to 0.75. So, option A is not our answer, because we're on the hunt for the non-equivalent fraction. It's important to go through each option methodically like this to ensure we don't make any hasty decisions. Sometimes, the answer jumps out at you, but it's always good to double-check! Remember, in math, precision is key, and taking the time to simplify or convert can save you from making mistakes. Now, let's move on to the next option and see if it's the imposter we're looking for!

Evaluating Option B: $\frac{9}{12}$

Next up is option B: $\frac{9}{12}$. Just like with option A, we can either simplify this fraction or convert it to a decimal to see if it's equivalent to 0.75. Let's simplify $\frac{9}{12}$ first. The greatest common divisor of 9 and 12 is 3. So, we divide both the numerator and the denominator by 3: $\frac{9 \div 3}{12 \div 3} = \frac{3}{4}$. Look at that! $\frac{9}{12}$ simplifies to $\frac{3}{4}$, which, as we know, equals 0.75. If we convert $\frac{9}{12}$ to a decimal, we divide 9 by 12, and guess what? We get 0.75. So, $\frac{9}{12}$ is also equivalent to 0.75. Option B is not the fraction we're looking for; it's another member of the 0.75 club. We're narrowing down our options here, which is great! Each time we eliminate a choice, we get closer to finding the odd one out. This process of elimination is a valuable strategy in problem-solving. It helps you focus your attention on the remaining possibilities and increases your chances of finding the correct answer. Now, let's move on to option C and see if it's the non-equivalent fraction we've been searching for.

Evaluating Option C: $\frac{6}{9}$

Alright, let's tackle option C: $\frac{6}{9}$. As with the previous options, we'll simplify the fraction and convert it to a decimal to check for equivalence to 0.75. To simplify $\frac{6}{9}$, we find the greatest common divisor of 6 and 9, which is 3. Dividing both the numerator and the denominator by 3, we get $\frac{6 \div 3}{9 \div 3} = \frac{2}{3}$. Now, this looks different from $\frac{3}{4}$! Let's convert $\frac{2}{3}$ to a decimal. Dividing 2 by 3, we get approximately 0.666... (a repeating decimal). This is definitely not equal to 0.75. So, we've found our culprit! $\frac{6}{9}$ is not equivalent to 0.75. It's the imposter, the odd one out. We can stop here, but for completeness, let's check option D as well. Identifying the correct answer often involves recognizing a pattern or a difference. In this case, simplifying $\frac{6}{9}$ immediately showed us that it wasn't going to match our target value of 0.75. This highlights the importance of simplifying fractions whenever possible; it can quickly reveal whether or not they are equivalent.

Evaluating Option D: $\frac{3}{4}$

Finally, let's examine option D: $\frac{3}{4}$. Well, this one is pretty straightforward! We already know that $\frac{3}{4}$ is equal to 0.75 (we established this when we converted 0.75 to a fraction). So, option D is definitely equivalent to 0.75. This confirms that our answer is indeed option C. We've checked all the options, and we're confident in our solution. Even though we had already identified the correct answer, it's always a good practice to check all the available choices, especially in timed tests or exams. This ensures that you haven't made any oversight. By confirming that $\frac{3}{4}$ is equivalent to 0.75, we can be absolutely sure that $\frac{6}{9}$ is the only fraction that is not equivalent to 0.75.

Conclusion

So, the fraction that is not equivalent to 0.75 is C. $\frac{6}{9}$. We found this by simplifying each fraction and converting them to decimals. Hope you had fun cracking this problem with me! Remember, understanding equivalent fractions and being able to convert between fractions and decimals are super useful skills in math. Keep practicing, and you'll become a fraction master in no time!