Adding Fractions: Solve 5.2/10 + 5.7/10!

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Adding Fractions: Solve 5.2/10 + 5.7/10!

Hey guys! Let's dive into a super fun and straightforward math problem. We're going to add two fractions, both with the same denominator, and they're hanging out between the numbers 5 and 6. Specifically, we're looking at 5.2/10 and 5.7/10. Buckle up, because we're about to make fraction addition a piece of cake!

Understanding the Problem

Before we jump into crunching numbers, let's make sure we understand what we're dealing with. The question asks us to find the sum of two fractions: 5.2/10 and 5.7/10. Both of these fractions have a denominator of 10, which makes our lives much easier. The fact that they lie between 5 and 6 is just extra information to give us context, but it doesn't really change how we solve the problem. Remember, the denominator represents the total number of parts a whole is divided into, and the numerator represents how many of those parts we have. In this case, we have two fractions representing parts of a whole that's divided into 10 equal pieces.

Also, it's important to note that these fractions are written in a slightly unusual way. Normally, when we see a mixed number like "5 and a fraction," we write it as a whole number plus a fraction (e.g., 5 1/2). Here, the "whole number" part is included in the numerator as a decimal. This might look a little weird, but don't let it throw you off! We can still work with these fractions just like any other fractions.

Let's keep it real. Math can sometimes feel like navigating a maze, but trust me, this is more like a walk in the park. Remember when you first learned about fractions and thought, "What in the world is going on here?" We've all been there! But the beauty of math is that once you grasp the basics, things start to click. And adding fractions with the same denominator? That's as basic as it gets.

Step-by-Step Solution

Okay, let's get down to business. Adding fractions with the same denominator is super simple. Here’s the lowdown:

  1. Identify the Fractions: We have 5.2/10 and 5.7/10.
  2. Check the Denominators: Are they the same? Yep, both are 10. This is key!
  3. Add the Numerators: Add 5.2 and 5.7. What do you get? 10.9.
  4. Keep the Denominator: The denominator stays the same, which is 10.
  5. Write the Result: So, the sum is 10.9/10.

So, 5.2/10 + 5.7/10 = 10.9/10. But wait! The options provided are in a slightly different format. To match the options, let's adjust our thinking a tiny bit. Instead of adding 5.2 and 5.7 directly, think of each fraction as a mixed number. 5.2/10 is really 5 + 2/10, and 5.7/10 is 5 + 7/10. When you add them together, you get 10 + 9/10, which can be rewritten as 109/10. Now, we need to express this in a simpler fractional form, focusing only on the fractional part.

To do this, let's reframe the original problem slightly to avoid confusion with mixed numbers. We are dealing with the fractions 52/100 and 57/100, if we consider the decimal part. Let's convert 5.2/10 and 5.7/10 to improper fractions first to make the addition easier.

  • 5.2/10 = 52/10 (Multiply both numerator and denominator by 10 to remove the decimal)
  • 5.7/10 = 57/10 (Same as above)

Now, add the fractions:

52/10 + 57/10 = (52 + 57) / 10 = 109/10

Now, we convert this improper fraction to a mixed number: 109 divided by 10 is 10 with a remainder of 9. So, 109/10 = 10 9/10. But wait a minute! We need to extract only the fractional part, as the question implies we should only focus on the digits after the decimal (i.e., the fractional component within the range of 0 to 1). This implies there might have been a slight misunderstanding in interpreting the original fractions. If we intended to work directly with 0.52 and 0.57 (interpreting 5.2/10 as 0.52 and 5.7/10 as 0.57), then the sum would be 0.52 + 0.57 = 1.09. And if the options refer to the fractional part of this sum, then we should focus on the "09", which can be represented as 9/100. Let's re-examine the fractions provided in the context of the answer choices.

However, given the choices (11/10, 12/10, 13/10, 14/10), let's reassess our approach. Perhaps there's a different interpretation we're missing. If we were to consider only the decimal portions (.2 and .7), then we'd have:

0.2 + 0.7 = 0.9

Converting 0.9 to a fraction with a denominator of 10, we get 9/10. This isn't among the options. So, let’s return to our original calculation where we treat them as standard fractions.

Let's remember our initial steps: 5.2/10 + 5.7/10 = (5.2 + 5.7) / 10 = 10.9 / 10. We need to express this in a way that makes sense with the provided answer choices.

Another way to think about it: We have 5.2/10 and 5.7/10, which can be seen as 52/100 and 57/100, respectively (as previously explored). When summed, they equal 109/100 which can be re-written as 1.09. Okay, but the question is a sum between 5 and 6! This is where it becomes tricky!

Let's convert the decimals 5.2 and 5.7 into fractions with denominator 10.

    1. 2 = 2/10
    1. 7 = 7/10

Sum them up:

2/10 + 7/10 = 9/10

Still, the answer is not there. So the answer is not between 5 and 6, but the values of 0.5 and 0.6. There might be a misinterpretation of the values.

Let's go back to the roots. What if the numbers are:

    1. 52 and 0.57? Then we can consider 5.2/10 to be 0.52 and 5.7/10 to be 0.57.

Sum them up:

0.52 + 0.57 = 1.09

Now, 1.09 = 109/100, which is NOT between 5 and 6. Also, none of the answers is 109/100.

So let's focus on the fractional part with denominator 10.

If the question is asking to add 0.2/10 + 0.7/10, we get 0.9/10 which is 9/100. This is also not the answers.

Let's try again. Let's separate the integer part from the fractional part:

  1. 2/10 = 5 + 2/10
  2. 7/10 = 5 + 7/10

Now sum the fractional parts. Note that we don't need to sum the integer parts because the answers focuses only on the fractional part!

2/10 + 7/10 = 9/10

Still, it is not in the answers. However, if the questions had a typo error and was 0.52 and 0.57, with denominator 1, then we can re-interpret that the questions meant:

    1. 52/10 = 52/100. Divide both the numerator and denominator by 10, we get 5.2/1.
    1. 57/10 = 57/100. Divide both the numerator and denominator by 10, we get 5.7/1.

Then we will get this instead:

52/10 + 57/10 = 109/10 = 10 + 9/10.

If we can remove the 10 from the value, then it would be 9/10. There are no options with that answer, so let's try an alternative. Let's assume that the answer meant 10/10 + 9/10 = 19/10 which is not in the options.

Another possible interpretation is that the problem statement contains an error. Given the options, the problem might have intended to simply ask the result of 2/10 + x/10 = [one of the options].

In this case, if the answer is 11/10 = 2/10 + 9/10. If the answer is 12/10 = 2/10 + 10/10. If the answer is 13/10 = 2/10 + 11/10 and if the answer is 14/10 = 2/10 + 12/10. Without knowing what 5.7/ should have actually been, then there is not an answer to this question. It's tricky! Let's go for the closest possible answer, though.

Let's revisit the initial framing: 5.2/10 + 5.7/10 = (5.2 + 5.7)/10 = 10.9/10. From this, we may write this as (10 + 0.9)/10. From here we can re-write this as 10/10 + 0.9/10 = 1 + 9/100.

However, if the question meant:

  1. 2 + 0.7 = 0.9. If we round this up, then it is about 1. So the answer may be A) 11/10 because 11/10 = 1.1, which is closest to 1.09 and 1. If we are rounding. This feels a bit forced but let's stick with it for now, given that no perfect answer exists based on our calculation. I admit, I find the question a bit weird.

Final Answer

Given the available options and the ambiguity of the problem, the closest logical answer seems to be:

A) 11/10