Math Problem Solver: 5 11/12 - (2 13/10 + 1 3/20)

Hey guys! Are you scratching your heads over this math problem: 5 11/12 - (2 13/10 + 1 3/20)? Don't worry, I'm here to break it down for you step-by-step. We're going to tackle this mixed number subtraction problem together, ensuring you understand each move. Let's get started and make math a little less intimidating, alright?

Breaking Down the Problem: Understanding Mixed Numbers

First things first, let's understand what we're dealing with. The problem involves mixed numbers, which are numbers that combine a whole number and a fraction. For example, in "5 11/12", '5' is the whole number, and '11/12' is the fraction. We need to perform the operation inside the parentheses first, following the order of operations (PEMDAS/BODMAS). This means we'll add 2 13/10 and 1 3/20 before subtracting the result from 5 11/12. It's like a mathematical puzzle; each step brings us closer to the solution. The core of this problem lies in fraction arithmetic – adding and subtracting fractions specifically. We'll need to find common denominators, add or subtract the numerators, and simplify our answers. Understanding mixed numbers is crucial because they're essentially a shorthand way of representing a number that isn't a whole unit. They represent a quantity that is more than a whole number, but not quite a whole number more. In our case, we're not just dealing with whole numbers; we're dealing with parts of wholes as well. Therefore, careful attention to the fraction part is crucial to get the correct answer. So, buckle up, and let's unravel this step by step, making sure every concept is clear and easy to follow. Remember, practice makes perfect, and with a little patience, you'll be acing these problems in no time! Also, remember that fractions are simply division problems in disguise, so keep that in mind as we proceed!

Step-by-Step Solution: Adding Fractions Inside Parentheses

Now, let's focus on the part inside the parentheses: (2 13/10 + 1 3/20). Our goal here is to combine these two mixed numbers. The first thing we need to do is add the whole numbers together and then add the fractional parts.

Let's start by adding the whole numbers: 2 + 1 = 3. Great!

Now, for the fractions: 13/10 + 3/20. To add these, we need a common denominator. The least common multiple (LCM) of 10 and 20 is 20. So, we'll convert 13/10 to an equivalent fraction with a denominator of 20.

To do this, multiply the numerator and the denominator of 13/10 by 2, which gives us 26/20. Now, we can add the fractions: 26/20 + 3/20 = 29/20.

However, 29/20 is an improper fraction (the numerator is larger than the denominator), so we can simplify it to a mixed number. 29 divided by 20 is 1 with a remainder of 9, so 29/20 = 1 9/20.

Now, combine the whole number we got from adding the original whole numbers (3) with the mixed number from the fractions (1 9/20). 3 + 1 9/20 = 4 9/20. Thus, the sum of 2 13/10 + 1 3/20 = 4 9/20. See, it's not that scary, is it? Remember that the key is consistency and focus. Each step gets you closer to the answer. Keep practicing, and you will become proficient at adding and subtracting fractions and mixed numbers. The goal here is to be precise in each step, double-check your calculations, and make sure you're comfortable with converting between improper fractions and mixed numbers. Let's move on to the next and final step.

Final Calculation: Subtracting the Result

Alright, we're at the final stage! Now we need to subtract the result from the parentheses (4 9/20) from 5 11/12. So, we have 5 11/12 - 4 9/20. Just like before, we're going to work with whole numbers and fractions separately, so let's get it done.

First, we'll subtract the whole numbers: 5 - 4 = 1. Cool beans.

Now, let's handle the fractions: 11/12 - 9/20. To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 12 and 20 is 60. So, we need to convert both fractions to have a denominator of 60. For 11/12, we multiply both the numerator and denominator by 5, giving us 55/60. For 9/20, we multiply both the numerator and denominator by 3, giving us 27/60. Now we can subtract the fractions: 55/60 - 27/60 = 28/60.

But hold on, we can simplify the fraction 28/60 by dividing both the numerator and the denominator by their greatest common divisor, which is 4. This simplifies to 7/15. Now we combine the whole number and the simplified fraction: 1 + 7/15 = 1 7/15. This is our final answer! Thus, 5 11/12 - (2 13/10 + 1 3/20) = 1 7/15. That wasn't so bad, right? Always remember to simplify your fractions to their simplest form. Keep an eye on your calculations. Double-check your work, and you will gain confidence in your mathematical capabilities. It’s a process, but with each problem, you're building a stronger foundation.

Summary and Tips for Solving Similar Problems

So, to recap, we first addressed the parentheses by adding the mixed numbers inside. Then, we subtracted the result from the initial mixed number. We systematically worked through each step, paying close attention to the fractions and ensuring we had a common denominator before adding or subtracting. Always simplify your fractions! This keeps the numbers manageable and ensures your final answer is in its simplest form. When you're dealing with mixed numbers, remember to convert them to improper fractions if it helps you to visualize the problem better, but remember to convert back at the end, or you can work directly with the mixed numbers as we did. Always double-check your work, especially when dealing with fractions. Minor calculation errors can happen, so a quick review can save you from a wrong answer. Don't be afraid to practice. The more you solve these types of problems, the more comfortable you will become. Try different examples. This will improve your understanding and speed up your problem-solving skills. Remember that math is a language, and the more you use it, the better you get at it. So, keep practicing, and don't give up! And finally, make sure you understand the basics of fractions, like finding common denominators and simplifying fractions. This will be an important skill in solving future math problems!

I hope this step-by-step guide helps you understand how to solve this problem and similar problems in the future. If you have any questions, feel free to ask! Happy calculating!