Adding Fractions What To Add To 9/8 + 11/10 To Get 1

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Hey guys! Ever stumbled upon a math problem that looks a bit like a puzzle? Well, today we're diving into one of those! We're going to break down the question: "What should be added to $98+1110{\frac{9}{8}+\frac{11}{10}}$ to make 1?" Don't worry, it's not as scary as it looks. We'll go through it step by step, so you'll not only understand the answer but also why it's the answer. This isn't just about getting the right number; it's about understanding the process, which is super important in math. Think of it like this: we're not just building a house; we're learning how to read the blueprint too! So, grab your thinking caps, and let's get started!

Understanding the Problem

Okay, let's break down this math problem like pros! Our main goal here is crystal clear: We need to figure out what magical number, when added to the sum of $98+1110{\frac{9}{8}+\frac{11}{10}}$, will give us the ultimate result of 1. Sounds like a quest, right? To get there, we need to understand a few key things. First off, we've got two fractions hanging out in the brackets: $98{\frac{9}{8}}$ and $1110{\frac{11}{10}}$. These aren't just any numbers; they're fractions, which means they represent parts of a whole. Think of them like slices of a pizza, but in math form. Before we can even think about adding them to something to get 1, we need to know what their total value is. That's where the addition part comes in. We're essentially combining these two "pizza slices" to see how much we've got in total. Once we know that, we can then figure out how much more we need to reach our target – which, in this case, is the number 1. This "1" is our whole pie, our entire pizza. So, the question is, how much more do we need to complete the pie? This problem is a classic example of how math problems often require us to tackle them in stages. We can't jump straight to the answer; we need to follow a logical path, step by step. First, we add the fractions, then we figure out the difference between that sum and 1. It's like following a recipe – each step is important, and you can't skip ahead without messing things up. So, let's roll up our sleeves and get ready to add some fractions!

Step 1: Adding the Fractions $98{\frac{9}{8}}$ and $1110{\frac{11}{10}}$

Alright, team, let's dive into the nitty-gritty of adding these fractions! We've got $98{\frac{9}{8}}$ and $1110{\frac{11}{10}}$, and our mission is to combine them into one single fraction. But, here's the catch: we can't just add the top numbers (numerators) and the bottom numbers (denominators) separately. Fractions have a golden rule: You can only add them if they have the same denominator. Think of it like trying to add apples and oranges – you need to convert them to the same unit (like "fruit") before you can add them together meaningfully. So, how do we get our fractions to speak the same language? We need to find what's called the least common denominator (LCD). The LCD is the smallest number that both denominators (8 and 10 in our case) can divide into evenly. It's like finding a common meeting point for our fractions. To find the LCD, we can list out the multiples of each denominator and see where they first overlap. For 8, the multiples are: 8, 16, 24, 32, 40, ... For 10, the multiples are: 10, 20, 30, 40, ... Aha! We've found our LCD: it's 40. Now that we have the LCD, we need to convert each fraction so that it has a denominator of 40. We do this by multiplying both the numerator and the denominator of each fraction by the same number. For $98{\frac{9}{8}}$, we need to multiply the denominator (8) by 5 to get 40. So, we also multiply the numerator (9) by 5, giving us $4540{\frac{45}{40}}$. For $1110{\frac{11}{10}}$, we need to multiply the denominator (10) by 4 to get 40. So, we also multiply the numerator (11) by 4, giving us $4440{\frac{44}{40}}$. Now we're cooking! Our problem has transformed into $4540+4440{\frac{45}{40} + \frac{44}{40}}$. Since the denominators are the same, we can finally add the numerators. 45 + 44 equals 89. So, the sum of our fractions is $8940{\frac{89}{40}}$. We've successfully added the fractions! But remember, we're not done yet. We've just completed the first part of our quest. Now we need to figure out what to add to this sum to get 1.

Step 2: Finding the Difference Between $8940{\frac{89}{40}}$ and 1

Okay, mathletes, we've conquered the fraction addition, and now it's time for the next challenge! We've figured out that $98+1110=8940{\frac{9}{8} + \frac{11}{10} = \frac{89}{40}}$. Awesome job! But remember our original mission? We need to find out what to add to this sum to make 1. So, we're essentially asking: $8940{\frac{89}{40}}$ + ? = 1. This is where subtraction comes into play. To find the missing piece, we need to subtract $8940{\frac{89}{40}}$ from 1. It's like having a whole pizza (that's our 1) and eating $8940{\frac{89}{40}}$ of it. How much pizza is left? To do this subtraction, we need to think of 1 as a fraction with the same denominator as $8940{\frac{89}{40}}$. Remember, any number divided by itself is 1. So, we can rewrite 1 as $4040{\frac{40}{40}}$. Now our problem looks like this: $4040−8940{\frac{40}{40} - \frac{89}{40}}$. Uh oh! We've got a slight issue. We're trying to subtract a larger number (89) from a smaller number (40). This means our answer will be a negative fraction. But don't panic! This is perfectly fine, and it just means that $8940{\frac{89}{40}}$ is actually more than 1. So, to get from $8940{\frac{89}{40}}$ back down to 1, we'll need to add a negative number. Let's do the subtraction: 40 - 89 = -49. So, $4040−8940=−4940{\frac{40}{40} - \frac{89}{40} = \frac{-49}{40}}$. This means that we need to add $−4940{\frac{-49}{40}}$ (or subtract $4940{\frac{49}{40}}$) from $8940{\frac{89}{40}}$ to get 1. Another way to think about it is that $8940{\frac{89}{40}}$ is $4940{\frac{49}{40}}$ more than 1. We're in the home stretch now! We've found the missing piece. But let's take a moment to recap what we've done and make sure we fully understand the answer.

The Final Answer: $−4940{\frac{-49}{40}}$

Drumroll, please! We've reached the end of our mathematical quest, and it's time to reveal the answer. After all our calculations and brain-teasing, we've discovered that we need to add $−4940{\frac{-49}{40}}$ to $98+1110{\frac{9}{8} + \frac{11}{10}}$ to get 1. In other words, $−4940{\frac{-49}{40}}$ is the magic number that completes our equation. But wait, let's not just box up the answer and call it a day. It's super important to understand why this is the answer. Remember, we started with the sum of two fractions, $98{\frac{9}{8}}$ and $1110{\frac{11}{10}}$. We added those together and got $8940{\frac{89}{40}}$. Then, we realized that $8940{\frac{89}{40}}$ is actually greater than 1. It's like having more than a whole pizza! So, to get back down to 1, we needed to subtract the extra amount. That extra amount turned out to be $4940{\frac{49}{40}}$, which, in our equation, translates to adding $−4940{\frac{-49}{40}}$. This negative fraction is the key to balancing the equation and bringing the total back to 1. So, the final answer isn't just a number; it's a solution that makes perfect mathematical sense. We've not only found the answer, but we've also understood the journey to get there. Give yourselves a pat on the back, math wizards! You've tackled this problem like true champions.

Why This Matters: Real-World Applications

Okay, we've cracked the math problem, which is awesome! But you might be thinking, "When am I ever going to use this in real life?" That's a totally valid question, and I'm here to tell you that understanding fractions and how they work is actually super useful in a ton of everyday situations. Think about it: fractions are everywhere! Cooking, for example. Recipes often call for amounts like $12{\frac{1}{2}}$ cup of flour or $34{\frac{3}{4}}$ teaspoon of salt. If you don't understand how to add and subtract fractions, you might end up with a cake that's a disaster! Managing money is another area where fractions are essential. Splitting a bill with friends? Calculating discounts at the store (like 25% off)? Figuring out interest rates on a loan? All of these involve working with fractions and percentages, which are just fractions in disguise. Even in fields like construction and engineering, fractions are crucial. Measuring materials, calculating angles, and ensuring things fit together perfectly often require precise knowledge of fractions. Imagine building a house where the measurements are off – that could be a recipe for disaster! The core skill we used in our problem – figuring out how much more we need to reach a goal – is also a valuable life skill. Whether it's saving up for a new gadget, reaching a fitness goal, or completing a project at work, understanding how to break down a problem into smaller steps and track your progress is essential. So, while our math problem might seem abstract, the underlying concepts are incredibly practical. By mastering fractions, you're not just acing math tests; you're building a foundation for success in many areas of life. Keep up the great work, guys!

Conclusion

Alright, superstars, we've reached the end of our fraction-filled adventure! We started with a seemingly simple question: "What should be added to $98+1110{\frac{9}{8} + \frac{11}{10}}$ to make 1?" But, as we discovered, there's a whole world of mathematical concepts hiding beneath the surface. We learned how to add fractions by finding the least common denominator, how to subtract fractions from whole numbers, and how to interpret negative fractions in the context of a problem. More importantly, we learned how to break down a complex problem into smaller, more manageable steps. This is a skill that will serve you well not just in math class, but in all areas of life. We also explored why understanding fractions is so important in the real world, from cooking and managing money to construction and engineering. Fractions aren't just abstract numbers; they're the building blocks of many practical skills. So, what's the takeaway from all of this? Math isn't just about memorizing formulas and getting the right answers. It's about understanding the underlying concepts, developing problem-solving skills, and learning how to think critically. And, let's be honest, it can even be kind of fun! Remember, every math problem is like a puzzle waiting to be solved. Don't be afraid to get your hands dirty, experiment with different approaches, and learn from your mistakes. And most importantly, never stop asking "why?" The more you understand the "why" behind the math, the more confident and successful you'll become. So, keep practicing, keep exploring, and keep challenging yourselves. You've got this!