1. The problem asks to find the fraction represented by point B on a number line. 2. The number line has points at 3/4, B, -1/2, 1/4, C, and 0, with B located between 3/4 and -1/2. 3. To find B, we note that 3/4 is 0.75 and -1/2 is -0.5. 4. Since B is between 3/4 and -1/2, we find the midpoint to estimate B's value. 5. The midpoint formula for two numbers $a$ and $b$ is $$\frac{a+b}{2}$$. 6. Applying this, $$B = \frac{\frac{3}{4} + \left(-\frac{1}{2}\right)}{2} = \frac{\frac{3}{4} - \frac{1}{2}}{2}$$. 7. Find common denominator for numerator: $$\frac{3}{4} = \frac{6}{8}, \frac{1}{2} = \frac{4}{8}$$. 8. So numerator is $$\frac{6}{8} - \frac{4}{8} = \frac{2}{8} = \frac{1}{4}$$. 9. Now, $$B = \frac{\frac{1}{4}}{2} = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}$$. 10. Therefore, point B represents the fraction $\frac{1}{8}$.