Math Problem: 3 2/5 + (-2.5) - (-4 1/3) Solved!

Hey guys! Let's dive into solving the math problem: 3 2/5 + (-2.5) - (-4 1/3). This looks a bit intimidating at first glance, with fractions and decimals all mixed up, but trust me, we can break it down step by step and make it super easy. The goal here is to arrive at the correct answer. We'll convert fractions to decimals, handle the negative signs like pros, and do some basic addition and subtraction. Ready to get started? Let’s break down the whole process, so you can solve problems like this with ease! So, first things first, let's look at the given expression: 3 2/5 + (-2.5) - (-4 1/3). We need to simplify it, and we'll do this by converting all the numbers to either decimals or fractions. I'll show you both ways, so you can choose which one feels easier for you. Remember, the key is to stay organized and take it one step at a time.

Step 1: Converting Mixed Numbers and Fractions to Decimals

Alright, the first step is to convert the mixed number and the fraction into decimals to make our calculations easier. We've got two numbers in the expression that need conversion: 3 2/5 and 4 1/3. Let’s deal with these guys first. Converting 3 2/5 to a decimal is straightforward. First, you need to understand that 2/5 means “two divided by five”. So, do the math: 2 divided by 5 equals 0.4. Now, add the whole number part, which is 3. So, 3 2/5 becomes 3 + 0.4 = 3.4. Awesome, right? Next up is 4 1/3. Here, 1/3 means “one divided by three.” When you do this division, you get 0.3333… and it keeps going. Since it's a repeating decimal, we'll round it to the nearest hundredth, so 1/3 is approximately 0.33. Add the whole number 4, and you get 4.33 (approximately). At this point, you've turned the mixed number and the fraction into decimals. This allows us to work with numbers that are easier to add and subtract. Keep in mind that when dealing with repeating decimals, like in the case of 1/3, we round to maintain accuracy. This step is about getting everything on a level playing field, making sure that everything we use is something we can directly calculate. Keep in mind: Practice makes perfect. Keep doing this until you get it.

Now our expression looks like this: 3.4 + (-2.5) - (-4.33) (approximately).

Step 2: Handling Negative Signs

Okay, next up, let's deal with those negative signs. Remember, subtracting a negative number is the same as adding a positive number. In other words, - (-x) becomes + x. Let's clarify what this means. In our original equation, we have - (-4.33). This translates to + 4.33. Always keep an eye out for double negatives, since they are easy to overlook. Double negatives can be a little tricky. They're like mathematical ninjas, trying to confuse you! So, the expression simplifies to 3.4 + (-2.5) + 4.33. Nice, right? Now that we've cleared up the negative signs, let's work on the actual math.

Think of it this way: when you subtract a negative, you’re essentially adding the positive version of that number. It is one of the most common mathematical rules, which needs to be carefully examined. Now, our expression looks much simpler and easier to manage. Handling negative signs is a crucial part of working with integers, and mastering this part is very helpful. Always remember: a negative number subtracted from a negative number equals a positive number. Now, let’s go to the next step.

Step 3: Performing the Addition and Subtraction

Here’s where the actual calculation happens. Now that we have the cleaned expression: 3.4 + (-2.5) + 4.33, let’s add the numbers. Start by adding 3.4 and -2.5. Since we're adding a negative number, we're essentially subtracting 2.5 from 3.4. That gives us 0.9. Finally, add the remaining 4.33 to 0.9. So, 0.9 + 4.33 = 5.23. And that, my friends, is our answer! By breaking down the problem into smaller parts, it becomes much easier to manage. Now let's calculate everything.

• 3.4 + (-2.5) = 0.9
• 0.9 + 4.33 = 5.23

So the answer to 3 2/5 + (-2.5) - (-4 1/3) is approximately 5.23. We converted the mixed number and the fractions into decimals, simplified the negative signs, and performed the addition and subtraction. Remember to always work step by step and double-check your work, and you will become a pro at this. It’s all about breaking down the problem into manageable steps and knowing your basic math rules. Always remember that, by practicing, you'll become more confident in solving math problems. The secret? Patience and consistency! Keep practicing, and you'll nail it. Now let’s recap all the steps.

Step 4: Recap

Let's recap the whole process to make sure we've got it all down. First, convert mixed numbers and fractions to decimals. Next, simplify the equation by resolving negative signs. Finally, perform the addition and subtraction, carefully. Keep in mind, when you start with more complex problems, it might seem difficult at the beginning. But the same concepts apply, so don’t give up. The more problems you solve, the more confident you will become. Make sure to keep your steps clear and organized. Here are the main steps that we have followed:

1. Conversion: Convert mixed numbers and fractions to decimals. 3 2/5 becomes 3.4 and -4 1/3 becomes -4.33 (approximately).
2. Negative signs: Handle the double negative: - (-4.33) becomes + 4.33.
3. Addition and Subtraction: 3.4 + (-2.5) + 4.33 = 5.23.

So, the answer is approximately 5.23. The most important thing is to take your time and break down the problem step by step. That's the key to success. Remember, practice makes perfect. Keep up the great work!

Alternative Solution: Using Fractions

For those of you who prefer working with fractions, we can also solve this problem using that approach. Here’s how you do it, guys. Instead of converting everything to decimals, we’ll stick with fractions. This method can sometimes feel a bit more involved, but it's just as valid. Let's do it! First, convert the mixed numbers to improper fractions. 3 2/5 becomes 17/5. And 4 1/3 becomes 13/3. Now, we have 17/5 + (-2.5) - (-13/3). Next convert -2.5 to a fraction. Because -2.5 is the same as -5/2, so the equation now looks like this: 17/5 + (-5/2) + 13/3. Next, we need to find a common denominator for all the fractions. The least common multiple (LCM) of 5, 2, and 3 is 30. So, we'll convert all fractions to have a denominator of 30. Now let's transform the fractions, to the denominator of 30. We multiply the numerator and denominator to get: (17/5) * (6/6) = 102/30, (-5/2) * (15/15) = -75/30, (13/3) * (10/10) = 130/30. Now, let's substitute those equivalent fractions back into our equation: 102/30 + (-75/30) + 130/30. Now, combine the numerators: 102 - 75 + 130 = 157. Therefore, our answer is 157/30. To convert this back to a decimal, divide 157 by 30, and you will get 5.2333… which is approximately 5.23. This is approximately the same as our previous answer. Using fractions is a solid strategy. It helps you understand the essence of each number, providing a good perspective. Remember that both approaches, fractions and decimals, will lead you to the same correct answer. Always remember: in math, there are often multiple ways to reach the right solution. Keep that in mind!

Conclusion

And there you have it, guys! We've successfully solved the math problem 3 2/5 + (-2.5) - (-4 1/3). We did it two ways, by converting everything to decimals and by using fractions. Both methods led us to the correct answer, which is approximately 5.23. I hope you found this guide helpful. Remember to always double-check your work, and take it one step at a time. The key is to practice and be patient. Keep up the fantastic work and happy calculating! If you enjoyed this, feel free to give it a like and leave a comment below with any questions you might have. See ya!