Calculate
Fraction 1
Fraction 2
Variable Key
Addition
Find the LCD, convert both fractions, then add numerators.
Subtraction
Same steps as addition, subtract numerators instead.
Multiplication
Multiply numerators together and denominators together.
Division
Multiply by the reciprocal of the divisor.
Simplification
Divide numerator and denominator by their GCD.
Adding fractions combines two or more parts of a whole. The key rule is that fractions must share the same denominator (bottom number) before their numerators (top numbers) can be added. This shared denominator is called the Least Common Denominator (LCD).
Tip: A quick LCD shortcut: multiply the two denominators together. This always works, though it might not give the smallest LCD.
- 1Find the Least Common Denominator (LCD) of both fractions
- 2Convert each fraction to an equivalent fraction with the LCD
- 3Add the numerators — keep the denominator the same
- 4Simplify the result by dividing by the Greatest Common Factor (GCF)
Adding mixed numbers
Add the whole number parts and fraction parts separately, then combine. For 2½ + 1⅓: whole parts 2+1=3, fractions ½+⅓=5/6, total = 3 5/6.
Result greater than 1
When the numerator exceeds the denominator, convert to a mixed number. 7/4 = 1¾.
| Denominators | LCD | Conversion multipliers |
|---|---|---|
| 2 and 3 | 6 | ×3 and ×2 |
| 2 and 4 | 4 | ×2 and ×1 |
| 3 and 4 | 12 | ×4 and ×3 |
| 4 and 6 | 12 | ×3 and ×2 |
| 5 and 6 | 30 | ×6 and ×5 |
| 6 and 8 | 24 | ×4 and ×3 |
Fun Fact
Ancient Egyptians only used "unit fractions" — fractions with 1 in the numerator (like 1/2, 1/3, 1/7). They expressed all other fractions as sums of these unit fractions.