Adding Unlike Fractions

Adding unlike fractions involves finding a common denominator and then adding the numerators. Here are the steps to add unlike fractions:

Step 1: Find the Common Denominator
To add two unlike fractions, you need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the fractions.

Example: Let's add 3/4 and 2/5.
The LCM of 4 and 5 is 20. Therefore, the common denominator is 20.

Step 2: Convert the Fractions
Convert both fractions to have the same denominator as the common denominator found in step 1.

Example:
To convert 3/4 to have a denominator of 20, multiply both the numerator and denominator by 5.
3/4 = (3 * 5) / (4 * 5) = 15/20

To convert 2/5 to have a denominator of 20, multiply both the numerator and denominator by 4.
2/5 = (2 * 4) / (5 * 4) = 8/20

Step 3: Add the Numerators
Now that both fractions have the same denominator, add the numerators together.

Example:
15/20 + 8/20 = (15 + 8) / 20 = 23/20

Step 4: Simplify (if necessary)
If the fraction can be simplified, simplify it by dividing both the numerator and denominator by their greatest common divisor.

Example:
23/20 cannot be simplified further, so the final answer is 23/20.

Visual Representation:
- Find the common denominator
- Convert both fractions to have the same denominator
- Add the numerators
- Simplify the fraction (if possible)

Key Points:
- Adding unlike fractions requires finding a common denominator.
- The common denominator is the LCM of the denominators.
- Convert both fractions to have the same denominator.
- Add the numerators and keep the denominator the same.
- Simplify the fraction, if needed, by dividing both numerator and denominator by their greatest common divisor.