Adding and Subtracting Fractions

Fractions with Like Denominators

When adding or subtracting fractions with the same denominator, we simply add or subtract the numerators and keep the denominator the same.

Examples:

• 1/4 + 2/4 = 3/4
• 5/6 - 2/6 = 3/6 = 1/2 (simplified)
• 3/8 + 4/8 = 7/8

Fractions with Unlike Denominators

When adding or subtracting fractions with different denominators, we need to:

1. Find a common denominator
2. Convert each fraction to an equivalent fraction with the common denominator
3. Add or subtract the numerators
4. Simplify the result if possible

Example: 1/3 + 1/4

1. Find common denominator: 12
2. Convert fractions:
   • 1/3 = 4/12
   • 1/4 = 3/12
3. Add numerators: 4/12 + 3/12 = 7/12

Finding Common Denominators

There are two main methods to find a common denominator:

1. Least Common Multiple (LCM)

The LCM of two numbers is the smallest number that is a multiple of both numbers. This is the preferred method as it results in simpler calculations.

Example: Find LCM of 4 and 6

• Multiples of 4: 4, 8, 12, 16, 20, ...
• Multiples of 6: 6, 12, 18, 24, ...
• LCM = 12

2. Product Method

Multiply the denominators together. This always works but may result in larger numbers that need more simplification.

Example: 1/3 + 1/4

• Common denominator = 3 × 4 = 12
• 1/3 = 4/12
• 1/4 = 3/12
• 4/12 + 3/12 = 7/12

Mixed Numbers

When adding or subtracting mixed numbers:

1. Add or subtract the whole numbers
2. Add or subtract the fractions
3. If the fraction result is improper, convert to a mixed number and add to the whole number

Example: 2 1/3 + 1 1/4

1. Add whole numbers: 2 + 1 = 3
2. Add fractions: 1/3 + 1/4 = 4/12 + 3/12 = 7/12
3. Final answer: 3 7/12

Practice Tips

• Always simplify your final answer
• Check if your answer makes sense (e.g., is it reasonable?)
• When subtracting, make sure the first fraction is larger than the second
• Use visual models to help understand the process
• Practice with both proper and improper fractions