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).
Pro Tip
A quick LCD shortcut: multiply the two denominators together. This always works, though it might not give the smallest LCD.
Did You Know?
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.