If (M) is the midpoint of (-\frac{5}{3}) and ( \frac{7}{3} ) on the number line, what is (M)?

Correct answer: ( \frac{1}{3} )

The direct answer is option A: \(1/3\). The midpoint of two numbers is their average, so add the endpoints and divide by 2: \(M=\frac{(-5/3)+(7/3)}2\). Since the denominators are already equal, combine the numerators: \(-5/3+7/3=2/3\). Then divide by 2: \((2/3)/2=(2/3)(1/2)=1/3\). Therefore option A is correct. Option B, \(2/3\), stops after adding the endpoints and forgets to divide by 2. Option C, 1, is not the average; it does not follow from the required calculation. Option D, \(-1/3\), has the wrong sign because the positive endpoint is larger in magnitude than the negative endpoint, so the midpoint must lie to the right of zero. As a check, \(1/3\) is equally distant from both endpoints. Memory cue: midpoint equals first point plus second point, all divided by 2.