Subtracting Fractions: Solve 4/6 - 1/6 Easily!

Hey there, math enthusiasts! Today, let's tackle a simple yet fundamental concept in mathematics: subtracting fractions. Specifically, we're going to solve and simplify the expression $\frac{4}{6}-\frac{1}{6}$. Don't worry; it's easier than it sounds! So, grab your pencils, and let's dive in!

Understanding Fractions

Before we jump into solving the problem, it's essential to have a solid understanding of what fractions represent. A fraction is a way to represent a part of a whole. It consists of two main components:

• Numerator: The number on the top of the fraction. It represents how many parts of the whole we have.
• Denominator: The number on the bottom of the fraction. It represents the total number of equal parts that make up the whole.

For example, in the fraction $\frac{4}{6}$, 4 is the numerator, and 6 is the denominator. This means we have 4 parts out of a total of 6 equal parts.

Solving $\frac{4}{6}-\frac{1}{6}$

Now that we've refreshed our understanding of fractions, let's solve the problem at hand: $\frac{4}{6}-\frac{1}{6}$. The great thing about this problem is that we are subtracting fractions with common denominators. When fractions have the same denominator, the process becomes straightforward.

Here's how we do it:

1. Check the Denominators: Ensure that both fractions have the same denominator. In this case, both fractions have a denominator of 6. Since the denominators are the same, we can proceed with the subtraction.
2. Subtract the Numerators: Subtract the numerator of the second fraction from the numerator of the first fraction. So, we have $4 - 1 = 3$.
3. Keep the Denominator: The denominator remains the same. It stays as 6.
4. Write the Result: Combine the result from step 2 (the new numerator) with the original denominator from step 3. This gives us $\frac{3}{6}$.

Therefore, $\frac{4}{6}-\frac{1}{6} = \frac{3}{6}$.

Simplifying the Fraction

While we've successfully subtracted the fractions, it's always a good practice to simplify the result if possible. Simplifying a fraction means reducing it to its lowest terms. In other words, we want to find the smallest possible numerator and denominator that still represent the same value.

To simplify $\frac{3}{6}$, we need to find the greatest common divisor (GCD) of the numerator (3) and the denominator (6). The GCD is the largest number that divides both numbers without leaving a remainder.

In this case, the GCD of 3 and 6 is 3. This is because 3 divides into 3 once (3 ÷ 3 = 1) and 3 divides into 6 twice (6 ÷ 3 = 2).

Now, we divide both the numerator and the denominator by the GCD:

• New Numerator: $3 ÷ 3 = 1$
• New Denominator: $6 ÷ 3 = 2$

So, the simplified fraction is $\frac{1}{2}$.

Therefore, $\frac{3}{6}$ simplified is $\frac{1}{2}$. This means that $\frac{4}{6}-\frac{1}{6} = \frac{1}{2}$.

Why Simplifying Matters

Simplifying fractions might seem like an extra step, but it's crucial for a few reasons:

• Clarity: Simplified fractions are easier to understand and compare. For example, $\frac{1}{2}$ is immediately recognizable as "one half," whereas $\frac{3}{6}$ might require a bit more thought.
• Consistency: In mathematics, it's standard practice to express answers in their simplest form. This ensures consistency and makes it easier for others to interpret your work.
• Further Calculations: When performing further calculations with fractions, using simplified fractions can make the process easier and reduce the risk of errors.

Real-World Applications

Understanding and manipulating fractions is not just an abstract mathematical concept; it has numerous real-world applications. Here are a few examples:

• Cooking and Baking: Recipes often use fractions to specify ingredient amounts. For example, you might need $\frac{1}{2}$ cup of flour or $\frac{1}{4}$ teaspoon of salt.
• Measuring: Fractions are used in various measuring contexts, such as measuring length ($\frac{1}{8}$ inch), weight ($\frac{3}{4}$ pound), and volume ($\frac{2}{3}$ liter).
• Time: We use fractions to represent parts of an hour. For example, 30 minutes is $\frac{1}{2}$ hour, and 15 minutes is $\frac{1}{4}$ hour.
• Finance: Fractions are used to calculate percentages and discounts. For example, a 25% discount is equivalent to $\frac{1}{4}$ of the original price.
• Construction: Fractions are crucial in construction for measuring and cutting materials accurately. Builders use fractions to ensure that structures are built to the correct dimensions.

Practice Problems

To solidify your understanding of subtracting and simplifying fractions, here are a few practice problems:

1. $\frac{5}{8}-\frac{1}{8}$
2. $\frac{7}{10}-\frac{2}{10}$
3. $\frac{9}{12}-\frac{3}{12}$

Remember to simplify your answers to their lowest terms!

Conclusion

And there you have it! Subtracting fractions with common denominators is a straightforward process. By following the steps outlined above and practicing regularly, you'll master this essential mathematical skill in no time. Remember to always simplify your answers to their lowest terms for clarity and consistency. Understanding fractions is not only important for academic success but also for navigating various real-world situations. Keep practicing, and you'll become a fraction master!

Want to learn more about fractions? Check out Khan Academy's fraction resources for more in-depth lessons and practice exercises.