Discussion
A fraction is such that when 3/4 is added to it, we get 1/3. What is the fraction?
Answer: C
The fraction is -5/12.
Let the fraction be x. Then
\[ \begin{aligned} x + \frac{3}{4} &= \frac{1}{3} \\ x &= \frac{1}{3} - \frac{3}{4} = \frac{4 - 9}{12} = -\frac{5}{12} \end{aligned} \]
Check: \(-5/12 + 9/12 = 4/12 = 1/3\). The positive 5/12 comes from dropping the minus sign, and would give 14/12 when 3/4 is added.
The other two options fail the same check: \(2/1 + 3/4 = 11/4\) and \(4/7 + 3/4 = 37/28\), both greater than 1, while the required sum 1/3 is less than 3/4, so the fraction must be negative.
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