Adding Fractions: A Step-by-Step Guide

Hey math enthusiasts! Ready to dive into the world of fractions? Today, we're going to tackle a common problem: adding fractions! Specifically, we'll be looking at $\frac{1}{6} + \frac{3}{6}$ and simplifying the result to its lowest terms. This is a fundamental concept in mathematics, so understanding it is super important. Let's break it down step by step, making sure everyone can follow along.

Understanding the Basics of Fraction Addition

Before we jump into the calculation, let's make sure we're all on the same page about the basics. Fractions represent parts of a whole. Think of a pizza cut into equal slices. Each slice is a fraction of the whole pizza. The bottom number of the fraction, called the denominator, tells you how many equal parts the whole is divided into. The top number, the numerator, tells you how many of those parts you have. In our example, $\frac{1}{6}$ means we have 1 part out of a total of 6 equal parts. $\frac{3}{6}$ means we have 3 parts out of the same 6 equal parts.

When adding fractions, there's a golden rule: the denominators must be the same. Luckily for us, in the problem $\frac{1}{6} + \frac{3}{6}$, the denominators are already the same! This makes our lives much easier. If the denominators weren't the same, we'd have to find a common denominator, which is a number that both denominators can divide into evenly. But, again, we're in luck this time. We can proceed directly to adding the numerators.

Now, let's get to the fun part: adding the numerators. This is as simple as it sounds. We take the numerators (the top numbers) and add them together. Remember, in our problem $\frac{1}{6} + \frac{3}{6}$, the numerators are 1 and 3. So, 1 + 3 = 4. We keep the same denominator (6), so the initial result of adding the fractions is $\frac{4}{6}$. Easy peasy, right? But we're not quite done yet. The question asks us to reduce the fraction to its lowest terms. That’s where the next step comes in, and it's important. We want to find the smallest equivalent fraction. Think of it like simplifying the fraction to its most basic form, and we'll cover that next.

Reducing Fractions to Lowest Terms

So, we've added our fractions and got $\frac{4}{6}$. Great job, everyone! But as we mentioned earlier, the final step is to reduce the fraction to its lowest terms. This means simplifying the fraction so that the numerator and denominator have no common factors other than 1. We do this by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD is the largest number that divides evenly into both the numerator and the denominator.

In our case, the fraction is $\frac{4}{6}$. The factors of 4 are 1, 2, and 4. The factors of 6 are 1, 2, 3, and 6. The greatest common factor of 4 and 6 is 2. Therefore, we'll divide both the numerator (4) and the denominator (6) by 2. 4 divided by 2 is 2, and 6 divided by 2 is 3. Thus, $\frac{4}{6}$ reduced to its lowest terms is $\frac{2}{3}$. Congratulations! You've successfully added the fractions and simplified the answer. Remember, reducing fractions to their lowest terms ensures that your answer is in the simplest and most understandable form. It’s like polishing your work to make it shine. It’s essential for clear communication in mathematics and is a skill that pops up repeatedly.

If you're feeling a little unsure, don't worry! This concept takes practice. Try working through some other fraction addition problems, simplifying the fractions, and finding the common factors. You'll be a fraction-adding pro in no time! Practice makes perfect, and with each problem, you'll become more comfortable with the process. This step-by-step approach makes it easier to digest each component.

Answering the Multiple-Choice Question

Now that we've gone through the whole process, let's look back at the multiple-choice options. We know that $\frac{1}{6} + \frac{3}{6} = \frac{4}{6}$, and when we reduce $\frac{4}{6}$ to its lowest terms, we get $\frac{2}{3}$.

• A. $\frac{1}{2}$ - This answer is incorrect. While $\frac{1}{2}$ is a simplified form, it is not the final simplified form for the original equation. Always ensure the final answer is simplified correctly to avoid this common mistake.
• B. $\frac{2}{3}$ - This is the correct answer. This is the result of adding $\frac{1}{6}$ and $\frac{3}{6}$ and reducing the sum to its lowest terms.
• C. $\frac{3}{6}$ - This answer is incorrect. This is the original fraction, and not the result of the entire calculation.
• D. $\frac{4}{6}$ - This is the initial result of the addition before simplification, therefore it is incorrect. Always remember the final step of simplification for this type of problem.

Therefore, the correct answer is B. $\frac{2}{3}$. Great job following along! Adding fractions and simplifying them to their lowest terms is a crucial skill, and you’ve now mastered it. Keep practicing, and you'll be well on your way to fraction mastery!