What is 9 5/6 plus 5 2/3?

• A. 14 7/12
• B. 15 1/2
• C. 16
• D. 15

Answer: (B)

Adding mixed numbers means lining up the parts so the fractional pieces share a common denominator, then combining them and drawing out any extra whole from the fractions.

Convert each mixed number to an improper fraction: 9 5/6 becomes 59/6, and 5 2/3 becomes 17/3. Change 17/3 to sixths to match: 17/3 = 34/6. Now add the fractions: 59/6 + 34/6 = 93/6, which simplifies to 31/2. Converting back to a mixed number gives 15 1/2.

You can also verify by adding the whole parts (9 + 5 = 14) and the fractional parts (5/6 + 2/3 = 5/6 + 4/6 = 9/6 = 3/2). The fractional sum is 1 and 1/2, so total is 14 + 1 + 1/2 = 15 1/2. The sum is 15 1/2.