Add 1/3 and 1/6. What is the sum?

Add 1/3 and 1/6. What is the sum?

• A. 1/6
• B. 1/2
• C. 2/3
• D. 1

Answer: (B)

When adding fractions with different denominators, you first find a common denominator and convert each fraction to an equivalent fraction with that denominator, then add the numerators and simplify. For 1/3 and 1/6, the smallest common denominator is 6. Convert 1/3 to 2/6 by multiplying top and bottom by 2. Now you have 2/6 + 1/6 = 3/6. This fraction simplifies by dividing top and bottom by 3, giving 1/2. So the sum is 1/2. A common slip is to add the numerators without changing to a common denominator, which would give 2/3 and misrepresent the combined amount. The correct method ensures both pieces are on the same-sized parts before combining.

When adding fractions with different denominators, you first find a common denominator and convert each fraction to an equivalent fraction with that denominator, then add the numerators and simplify.

For 1/3 and 1/6, the smallest common denominator is 6. Convert 1/3 to 2/6 by multiplying top and bottom by 2. Now you have 2/6 + 1/6 = 3/6. This fraction simplifies by dividing top and bottom by 3, giving 1/2. So the sum is 1/2.

A common slip is to add the numerators without changing to a common denominator, which would give 2/3 and misrepresent the combined amount. The correct method ensures both pieces are on the same-sized parts before combining.