Which of the following numbers could be added to 3/14 to make a sum greater than 1/2?
Responses
1/4
1/3
2/7
3/14
Let's examine each option to see which could be added to 3/14 to result in a sum greater than 1/2.
1. Adding 1/4 to 3/14:
\[ \frac{3}{14} + \frac{1}{4} = \frac{3}{14} + \frac{7}{28} = \frac{3 \times 2}{28} + \frac{7}{28} = \frac{6}{28} + \frac{7}{28} = \frac{13}{28} \]
Since 1/2 is equivalent to 14/28, and 13/28 is less than 14/28, this sum is not greater than 1/2.
2. Adding 1/3 to 3/14:
\[ \frac{3}{14} + \frac{1}{3} = \frac{3}{14} + \frac{14}{42} = \frac{3 \times 3}{42} + \frac{14}{42} = \frac{9}{42} + \frac{14}{42} = \frac{23}{42} \]
Since 1/2 is equivalent to 21/42, and 23/42 is greater than 21/42, this sum is greater than 1/2.
3. Adding 2/7 to 3/14:
\[ \frac{3}{14} + \frac{2}{7} = \frac{3}{14} + \frac{4}{14} = \frac{3+4}{14} = \frac{7}{14} \]
Since 7/14 simplifies to 1/2, this sum is exactly 1/2, not greater than 1/2.
4. Adding 3/14 to 3/14:
\[ \frac{3}{14} + \frac{3}{14} = \frac{3+3}{14} = \frac{6}{14} \]
Simplifying 6/14 gives us 3/7, which is still less than 1/2, so this sum is not greater than 1/2.
Therefore, the only option from the list that can be added to 3/14 to make a sum greater than 1/2 is 1/3.