How the Adding Fractions Calculator with Steps Method Works
To add fractions with different denominators, find the Least Common Denominator (LCD), convert each fraction into an equivalent fraction with that LCD, add the numerators, and simplify.
Core Formula:
\(\frac{a}{b} + \frac{c}{d} = \frac{a \cdot d + b \cdot c}{b \cdot d}\)
Key Rules & Steps:
- Find the Least Common Denominator (LCD / LCM) of both denominators.
- Multiply numerator and denominator of each fraction by the factor needed to match the LCD.
- Add the numerators together while keeping the common denominator unchanged.
- Reduce the resulting fraction to its simplest form by dividing by the Greatest Common Factor (GCF).
- If the result is an improper fraction, convert it to a mixed number if desired.
Worked Practice Examples:
Problem: 3/4 + 2/5
Result: 23/20 = 1 3/20
LCD of 4 and 5 is 20. (3 × 5)/(4 × 5) = 15/20 and (2 × 4)/(5 × 4) = 8/20. 15/20 + 8/20 = 23/20 = 1 3/20.
Problem: 1/6 + 2/3
Result: 5/6
LCD of 6 and 3 is 6. 2/3 becomes 4/6. 1/6 + 4/6 = 5/6 (already in simplest form).
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