Subtracting fractions with Different Denominators

Objective

Learn how to subtract fractions that have different denominators by finding a common denominator.

Steps to Subtract fractions

1. Find a Common Denominator: Identify the least common denominator (LCD) of the fractions.
2. Convert the fractions: Rewrite each fraction with the common denominator.
3. Subtract the Numerators: Perform the subtraction on the numerators while keeping the common denominator.
4. Simplify if Necessary: Reduce the fraction to its simplest form if possible.

Example

Subtract the fractions: $\frac{2}{3} - \frac{1}{4}$

Step 1: Find the Common Denominator

The denominators are 3 and 4. The least common denominator (LCD) is 12.

Step 2: Convert the fractions

• Convert $\frac{2}{3}$:
  $\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$
• Convert $\frac{1}{4}$:
  $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$

Step 3: Subtract the Numerators

Now, we subtract the numerators:
$\frac{8}{12} - \frac{3}{12} = \frac{8 - 3}{12} = \frac{5}{12}$

Step 4: Simplify if Necessary

In this case, $\frac{5}{12}$ is already in simplest form.

Key Questions

• What is the least common denominator for the fractions?
• How do you convert fractions to have a common denominator?
• What do you do after subtracting the numerators?

Conclusion

Subtracting fractions with different denominators involves finding a common denominator, converting the fractions, performing the subtraction, and simplifying the result if needed.