🔢 Operations with Fractions (Unlike Denominators)

The Problem with Unlike Denominators
You cannot add fractions that have different denominators directly:
• ½ + ⅓ = ❌ (can't add yet)

The Solution: Find a Common Denominator
The common denominator is a number that both denominators divide into evenly. The easiest is the Least Common Denominator (LCD).
Steps:
• Find the LCD (smallest number both denominators divide into)
• Convert each fraction to equivalent fraction with LCD
• Add or subtract the numerators
• Keep the denominator the same
• Simplify if needed

Example: ½ + ⅓
• LCD of 2 and 3 = 6
• ½ = 3/6
• ⅓ = 2/6
• 3/6 + 2/6 = (5)/(6)

Multiplying Fractions is EASY!
Unlike addition, you DON'T need common denominators. Just multiply straight across!
Rule: (a/b) × (c/d) = (a×c)/(b×d)
Steps:
• Multiply the numerators
• Multiply the denominators
• Simplify if needed

Example: ⅔ × ⅘ = (2×4)/(3×5) = 8/15
Multiplying Mixed Numbers:
• Convert mixed numbers to improper fractions
• Multiply straight across
• Convert back to mixed number

The "Keep-Change-Flip" Rule
Dividing fractions is easy with this trick:
Keep the first fraction
Change ÷ to ×
Flip the second fraction (reciprocal)
Rule: (a)/(b) ÷ (c)/(d) = (a)/(b) × (d)/(c) = (a × d)/(b × c)
Example: ¾ ÷ 2 = ¾ ÷ 2/1 = ¾ × ½ = (3)/(8)
Dividing Mixed Numbers:
• Convert mixed numbers to improper fractions
• Use Keep-Change-Flip
• Simplify