Adding Mixed Numbers: Step-by-Step Solutions

Hey guys! Let's dive into some mixed number addition problems. This is a super important skill in algebra, and honestly, it's pretty straightforward once you get the hang of it. We'll break down each problem step-by-step so you can totally nail it. We will be adding mixed numbers, which means we'll be dealing with whole numbers and fractions all mixed together. Don't worry, it's not as scary as it sounds. We'll treat the whole numbers and fractions separately, and then combine our results. Get ready to flex those math muscles! Let's get started with our first problem, and by the end, you'll be adding mixed numbers like a pro. Remember to always double-check your work, and don't be afraid to ask questions. Math is all about practice, and the more you practice, the better you'll become! So, grab your pencils and let's go. We'll start with a few basic examples to warm up, and then we'll tackle some slightly trickier ones. Are you ready to get started? Let's start with the first problem: 2rac{1}{3} + 1rac{2}{3}. This problem is a perfect warm-up, as it has fractions with the same denominator. This means that we can directly add the fractions and then add the whole numbers.

Problem A: 2rac{1}{3} + 1rac{2}{3}

Alright, let's break down this first one. The beauty of this problem is that the fractions already have the same denominator. This makes our lives way easier! When adding mixed numbers, the easiest approach is often to add the whole numbers separately and then add the fractions. Finally, combine everything for the final answer. Let's start by adding the whole numbers: 2 + 1 = 3. Cool, got that part down! Now, let's look at the fractions: rac{1}{3} + rac{2}{3}. Since the denominators (the bottom numbers) are the same, we can just add the numerators (the top numbers) and keep the denominator the same. So, 1 + 2 = 3. Therefore, rac{1}{3} + rac{2}{3} = rac{3}{3}. And guess what? rac{3}{3} is the same as 1! So, we have 3 (from the whole numbers) + 1 (from the fractions) = 4. That's it! The answer to 2rac{1}{3} + 1rac{2}{3} is 4. See? Not so bad, right? We just added the whole numbers, added the fractions, and then put it all together. Always remember the fundamental rules of fractions - same denominator, keep it; different denominator, common denominator. This is your first victory! Congrats on solving the first problem! Ready to move on to the next one? In addition to these problems, you can always practice more problems to perfect your understanding of mixed numbers. Feel free to explore other problem sets and exercises, as practice is key to mastering this concept. Now, let's see how you do with the next one.

Problem B: 1rac{4}{5} + rac{3}{5}

Alright, moving on to problem B: 1rac{4}{5} + rac{3}{5}. This one is a little different because we only have a whole number in the first mixed number. This also makes things super easy. Again, we can break this down into adding the whole numbers and the fractions separately. First, the whole number: we only have a 1 here, so that's easy! Now, let's add the fractions: rac{4}{5} + rac{3}{5}. Notice something cool? The denominators are the same! So, we can just add the numerators: 4 + 3 = 7. Thus, we have rac{7}{5}. Now, rac{7}{5} is an improper fraction (the numerator is bigger than the denominator), so we need to simplify it. We can rewrite rac{7}{5} as a mixed number: 1 rac{2}{5}. Remember, this means we can rewrite this as a whole number plus a fraction. Since the 5 fits once into 7 with a remainder of 2. So, we've got 1 (from the whole number) + 1 rac{2}{5} (from the fraction). Adding the whole numbers, 1 + 1 = 2. So, our final answer is 2 rac{2}{5}. You're crushing it! Remember, practice makes perfect. The more you do these, the faster and easier they'll become. Keep up the great work! With each problem you solve, you're building your confidence and strengthening your math skills. Always take your time, and don't be afraid to double-check your work. You're doing great, and I'm sure you can tackle any problem that comes your way. It is important to know how to rewrite an improper fraction into a mixed number. This is one of the most important concepts, as you need to be able to understand the different kinds of fractions.

Problem C: 2rac{1}{6} + 1rac{5}{12}

Okay, time for a slightly trickier one: 2rac{1}{6} + 1rac{5}{12}. Now, in this case, the denominators are not the same. This means we can't just add the fractions directly. We need to find a common denominator. The easiest way to do this is to find the least common multiple (LCM) of the denominators (6 and 12). In this case, the LCM is 12. So, let's rewrite our fractions with a denominator of 12. The second fraction already has a denominator of 12, so we don't need to change it. But for the first fraction, rac{1}{6}, we need to multiply both the numerator and the denominator by 2. That way, we will get a fraction with a denominator of 12. Doing that, we get rac{2}{12}. The fractions are rac{2}{12} + rac{5}{12}. Now, let's add the whole numbers: 2 + 1 = 3. Now let's add the fractions: rac{2}{12} + rac{5}{12} = rac{7}{12}. Finally, combine the whole number and fraction: 3 + rac{7}{12} = 3rac{7}{12}. Therefore, the answer to 2rac{1}{6} + 1rac{5}{12} is 3rac{7}{12}. We did it! Finding the common denominator is key here, and once you get the hang of it, you can solve these problems with ease. This problem is really meant to teach you the concept of common denominators. Without this concept, adding and subtracting fractions would be extremely difficult. We are almost done, and you will learn about the last one which is a little more tricky!

Problem D: 3rac{7}{7} + 1rac{5}{14}

Last one, let's go! 3rac{7}{7} + 1rac{5}{14}. Okay, this one has a little twist. Notice that rac{7}{7} is the same as 1! So, 3rac{7}{7} is the same as 4. Therefore, the problem is 4 + 1rac{5}{14}. Now, since 4 is a whole number, we just add the whole numbers: 4 + 1 = 5. We also have a fraction: rac{5}{14}. So, our final answer is 5rac{5}{14}. Boom! We've conquered all the problems. Always look for ways to simplify the fractions or whole numbers before you start adding. This will make the process easier. Excellent work, guys! You successfully navigated through adding mixed numbers. Keep practicing, and you'll become a total pro in no time. If you got stuck on one, that's okay! Review the steps, and try it again. You've got this!