Find the common denominator for 2/3 and 5/6.

• A. 3
• B. 6
• C. 9
• D. 12

Answer: (B)

A common denominator is a number that both denominators can divide into, and when adding or comparing fractions we usually use the smallest such number, called the least common denominator. For 2/3 and 5/6, the denominators are 3 and 6. The multiples of 3 are 3, 6, 9, … and the multiples of 6 are 6, 12, … The smallest shared multiple is 6, so 6 is the common denominator. Rewriting with this denominator: 2/3 becomes 4/6, and 5/6 stays 5/6. This makes it easy to combine or compare them (4/6 and 5/6 share the same bottom). While 12 would also work as a common denominator, 6 is the smallest one, which is why it’s preferred.