Which of the following fractions is equivalent to 0.75?

To determine which fraction is equivalent to 0.75, it’s helpful to first express 0.75 as a fraction. The number 0.75 can be rewritten as ( \frac{75}{100} ). This fraction simplifies by dividing both the numerator and the denominator by their greatest common divisor, which is 25.

When we divide the numerator 75 by 25, we get 3, and when we divide the denominator 100 by 25, we get 4. Therefore, ( \frac{75}{100} ) simplifies to ( \frac{3}{4} ).

This calculation shows that ( \frac{3}{4} ) represents the decimal 0.75 accurately. In terms of value, both representations describe the same quantity, and thus, ( \frac{3}{4} ) is equivalent to 0.75.

To further understand why the other fractions do not match, we can convert them or evaluate their decimal equivalents. For instance, ( \frac{1}{3} ) is approximately 0.333, ( \frac{4}{5} ) converts to 0.8, and ( \frac{2}{5}