Solving 5/6 - 1/2: A Step-by-Step Guide
Have you ever found yourself staring at a math problem involving fractions and felt a slight sense of panic? Don't worry, you're not alone! Fractions can seem a bit intimidating at first, but once you grasp the basic concepts, they become much more manageable. In this article, we're going to break down a common fraction subtraction problem: 5/6 - 1/2. We'll walk through the steps together, so by the end, you'll be a fraction-subtracting pro!
Diving into the Basics of Fraction Subtraction
Before we jump into the specific problem, let's quickly review the fundamentals of fraction subtraction. The most important thing to remember is that you can only subtract fractions if they have the same denominator. The denominator is the bottom number in a fraction, and it tells you how many equal parts the whole is divided into. Think of it like slicing a pizza: the denominator tells you how many slices you've cut the pizza into. To subtract fractions, you need to make sure your pizza slices are the same size!
If the fractions don't have the same denominator, we need to find a common denominator. This is a number that both denominators can divide into evenly. Once we have a common denominator, we can rewrite the fractions with this new denominator and then subtract the numerators (the top numbers). Let's see how this works in practice with our problem, 5/6 - 1/2.
Finding the Common Denominator
The first step in solving 5/6 - 1/2 is to find a common denominator for 6 and 2. One way to do this is to list the multiples of each denominator until we find a common one. The multiples of 6 are 6, 12, 18, 24, and so on. The multiples of 2 are 2, 4, 6, 8, 10, and so on. Notice that 6 appears in both lists! This means that 6 is a common denominator for 6 and 2. In fact, it's the least common denominator (LCD), which is the smallest common multiple of the denominators. Using the LCD makes our calculations easier.
Rewriting the Fractions
Now that we've found our common denominator, we need to rewrite the fractions with this denominator. The fraction 5/6 already has a denominator of 6, so we don't need to change it. However, we need to rewrite 1/2 with a denominator of 6. To do this, we need to multiply both the numerator and the denominator of 1/2 by the same number so that the denominator becomes 6. What number do we multiply 2 by to get 6? The answer is 3. So, we multiply both the numerator and the denominator of 1/2 by 3:
(1 * 3) / (2 * 3) = 3/6
Now we have rewritten 1/2 as 3/6. Our problem now looks like this: 5/6 - 3/6.
Subtracting the Fractions
With both fractions having the same denominator, we can finally subtract them! To subtract fractions with the same denominator, we simply subtract the numerators and keep the same denominator. So, we have:
5/6 - 3/6 = (5 - 3) / 6 = 2/6
Therefore, 5/6 - 1/2 = 2/6.
Simplifying the Result
We've found the answer, but it's always a good idea to simplify the fraction if possible. Simplifying a fraction means reducing it to its lowest terms. To do this, we need to find the greatest common factor (GCF) of the numerator and the denominator and divide both by it. The GCF of 2 and 6 is 2. So, we divide both the numerator and the denominator of 2/6 by 2:
(2 / 2) / (6 / 2) = 1/3
So, the simplified answer is 1/3. This means that 5/6 - 1/2 = 1/3.
Real-World Applications of Fraction Subtraction
Now that we've successfully subtracted the fractions, you might be wondering,
