Adding Fractions: A Step-by-Step Guide To Solving The Math Problem
Hey there, math enthusiasts! Let's dive into a fraction problem together. Today, we're going to solve: tres quintos (three-fifths) + dos tercios (two-thirds) + cuatro octavos (four-eighths). Don't worry if fractions seem a bit daunting at first; we'll break it down into easy-to-follow steps. This guide will help you understand how to add fractions and ensure that you can solve similar problems with confidence in the future. Ready? Let's get started!
Understanding the Basics: Fractions Explained
Before we jump into the calculations, let's quickly recap what a fraction is. A fraction represents a part of a whole. It's written as two numbers separated by a line, like this: a/b. The top number (a) is called the numerator, and it tells you how many parts you have. The bottom number (b) is the denominator, which tells you how many equal parts the whole is divided into. For example, in the fraction 1/2, the numerator is 1, and the denominator is 2. This means you have one part out of a total of two equal parts. In our problem, we are dealing with fractions like 3/5, 2/3, and 4/8. Understanding these basic components will set a strong base for solving more complex fraction-related problems.
When adding fractions, the most important thing is that the fractions have the same denominator, which is the common denominator. You can't directly add fractions unless they share a common denominator. So, the first step in adding fractions involves finding a common denominator, which is a number that all the denominators can divide into without any remainder. Then, you adjust each fraction so that all the fractions have the same denominator by multiplying the numerator and the denominator by the same number. After all the fractions have the same denominator, you can simply add the numerators, keeping the denominator the same. If the resulting fraction can be simplified, reduce it to its simplest form by dividing both the numerator and the denominator by their greatest common divisor.
Now, let's look at our problem: tres quintos + dos tercios + cuatro octavos. We have three fractions: 3/5, 2/3, and 4/8. As you can see, they all have different denominators. To solve this, we must make sure all the fractions have a common denominator. The common denominator, in this case, is the least common multiple (LCM) of the denominators. The LCM is the smallest number that is a multiple of all the given numbers. The LCM of 5, 3, and 8 is 120. Then, we need to transform each fraction so they all have the same denominator. Next, we'll perform some operations on the fractions to solve our math problem.
Step-by-Step Calculation: Solving the Problem
Okay, guys, let's break down the calculation step-by-step. First, we need to find a common denominator. The denominators in our fractions are 5, 3, and 8. The smallest number that all these numbers divide into evenly is 120. So, our common denominator will be 120. Remember, finding the common denominator is the most crucial step. It allows us to combine different fractions into one single fraction.
Now, we will adjust each fraction to have a denominator of 120. For the fraction 3/5, we need to multiply both the numerator and the denominator by a number that will result in the denominator being 120. To get from 5 to 120, we need to multiply by 24. So, we multiply both the numerator and denominator of 3/5 by 24:
(3/5) * (24/24) = 72/120
Next, let's work on 2/3. To get a denominator of 120, we multiply both the numerator and denominator by 40:
(2/3) * (40/40) = 80/120
Finally, we look at 4/8. To get a denominator of 120, we multiply the numerator and the denominator by 15:
(4/8) * (15/15) = 60/120
So now, our fractions look like this: 72/120, 80/120, and 60/120. Since all of them now have a common denominator, we can simply add the numerators together, keeping the denominator the same:
(72 + 80 + 60) / 120 = 212/120
That's the basic operation! But as a final step, we will simplify the resulting fraction to its lowest terms. Before we can give the answer, we have to simplify the fraction. In some cases, such as this one, you may need to simplify the fraction further. Simplifying a fraction means reducing it to its simplest form. You do this by dividing both the numerator and the denominator by their greatest common factor (GCF). The GCF is the largest number that divides evenly into both the numerator and the denominator.
Simplifying the Fraction
So, our final step is to simplify the fraction 212/120. Both 212 and 120 are divisible by 4. Divide both the numerator and the denominator by 4:
212 ÷ 4 = 53 120 ÷ 4 = 30
So, 212/120 simplifies to 53/30. This is an improper fraction because the numerator is larger than the denominator. You can also write this as a mixed number if you want (a whole number and a fraction). To do that, we divide 53 by 30. The result is 1 with a remainder of 23. So, 53/30 is the same as 1 and 23/30. That is your final answer!
Therefore, tres quintos + dos tercios + cuatro octavos = 53/30, or 1 and 23/30. Congratulations, you've successfully solved the fraction problem!
Conclusion: Practice Makes Perfect
Well done, everyone! You've successfully navigated through adding the fractions tres quintos + dos tercios + cuatro octavos. Remember, the key is to find the common denominator, adjust the fractions, add the numerators, and simplify if needed. Practice is key! The more you practice adding fractions, the more comfortable and confident you'll become. Try different fraction problems to build your skills and understanding. Don't be afraid to start with simpler problems and gradually work your way up to more complex ones. Keep practicing, and you'll master fractions in no time. If you encounter any issues, go back through the steps outlined in this guide. Feel free to revisit this guide as needed to reinforce your understanding.
Finally, keep in mind that understanding fractions is not just about getting the right answer; it's about building a solid foundation in mathematics. Fractions are fundamental concepts used in various areas, including algebra, geometry, and calculus. So, keep up the good work, and don't hesitate to ask questions or seek help if needed. You're doing great!
