How to Subtract Fractions with Different Denominators

Subtracting fractions can feel tricky, especially when they don't have the same bottom number (denominator). But don't worry! If we take it step by step, it's easier than it seems. Here’s a simple way to do it:

Step 1: Look at the Denominators

First, pay attention to the two fractions you want to subtract.

For example, let’s say we have $\frac{3}{4}$ and $\frac{1}{6}$.

Here, the denominators are 4 and 6.

Step 2: Find the Least Common Denominator (LCD)

Next, we need to find the least common denominator. This is the smallest number that both denominators can divide into evenly.

Let’s find it for 4 and 6:

• The multiples of 4 are: 4, 8, 12, 16, and so on.
• The multiples of 6 are: 6, 12, 18, and so forth.

The smallest number that appears in both lists is 12. So, our least common denominator is 12.

Step 3: Change Each Fraction

Now, we will change each fraction so that they both have the same denominator.

For $\frac{3}{4}$:

To change it to twelfths, we multiply the top (numerator) and the bottom (denominator) by 3.

$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$

For $\frac{1}{6}$:

To change this fraction to twelfths, we multiply the top and the bottom by 2.

$\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$

Step 4: Subtract the Fractions

Now that the fractions have the same denominator, we can subtract them easily.

So, we do:

$\frac{9}{12} - \frac{2}{12} = \frac{9 - 2}{12} = \frac{7}{12}$

Step 5: Simplify if You Can

Lastly, always check if the new fraction can be simplified.

In this case, $\frac{7}{12}$ is already in the simplest form, so we’re finished!

Summary

Remember these steps:

1. Identify the denominators.
2. Find the least common denominator.
3. Change the fractions.
4. Subtract.
5. Simplify if needed.

With a little practice, you’ll get really good at subtracting fractions!