How Do You Subtract Unlike Fractions?

To subtract unlike fractions, you must first find a common denominator before you can perform the subtraction.

Here's a breakdown of the process:

1. Identify the Unlike Fractions: Recognize that the fractions you're trying to subtract have different denominators. For example, 1/2 - 1/3.

2. Find the Least Common Multiple (LCM): Determine the least common multiple of the denominators. The LCM is the smallest number that both denominators divide into evenly. In our example (1/2 - 1/3), the denominators are 2 and 3. The LCM of 2 and 3 is 6.

3. Convert to Equivalent Fractions: Rewrite each fraction as an equivalent fraction with the common denominator (the LCM). To do this, divide the common denominator by the original denominator, and then multiply both the numerator and denominator of the original fraction by that result.

   • For 1/2: 6 / 2 = 3. So, (1 3) / (2 3) = 3/6
   • For 1/3: 6 / 3 = 2. So, (1 2) / (3 2) = 2/6

4. Subtract the Numerators: Now that the fractions have a common denominator, subtract the numerators. Keep the denominator the same.

   • 3/6 - 2/6 = (3 - 2) / 6 = 1/6

5. Simplify (if possible): Reduce the resulting fraction to its simplest form, if necessary. In our example, 1/6 is already in its simplest form.

Example:

Let's subtract 3/4 - 1/6.

1. Unlike Fractions: We have denominators 4 and 6.
2. LCM: The LCM of 4 and 6 is 12.
3. Equivalent Fractions:
   • 3/4 = (3 3) / (4 3) = 9/12
   • 1/6 = (1 2) / (6 2) = 2/12
4. Subtract: 9/12 - 2/12 = (9 - 2) / 12 = 7/12
5. Simplify: 7/12 is already in its simplest form.

Therefore, 3/4 - 1/6 = 7/12.