Which fractions are equivalent to \( \frac{1}{2} \) ? Hint: There may be more than one.

Fractions that are equivalent to \( \frac{1}{2} \) have numerators and denominators that are multiples of the original numerator and denominator. Here are several examples: 1. **Multiply both numerator and denominator by 2:** \[ \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \] 2. **Multiply both numerator and denominator by 3:** \[ \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \] 3. **Multiply both numerator and denominator by 4:** \[ \frac{1 \times 4}{2 \times 4} = \frac{4}{8} \] 4. **Multiply both numerator and denominator by 5:** \[ \frac{1 \times 5}{2 \times 5} = \frac{5}{10} \] 5. **Multiply both numerator and denominator by 6:** \[ \frac{1 \times 6}{2 \times 6} = \frac{6}{12} \] 6. **Multiply both numerator and denominator by 7:** \[ \frac{1 \times 7}{2 \times 7} = \frac{7}{14} \] 7. **Multiply both numerator and denominator by 8:** \[ \frac{1 \times 8}{2 \times 8} = \frac{8}{16} \] 8. **Multiply both numerator and denominator by 9:** \[ \frac{1 \times 9}{2 \times 9} = \frac{9}{18} \] 9. **Multiply both numerator and denominator by 10:** \[ \frac{1 \times 10}{2 \times 10} = \frac{10}{20} \] **General Form:** Any fraction of the form \( \frac{n}{2n} \), where \( n \) is a non-zero integer, is equivalent to \( \frac{1}{2} \). For example: - \( \frac{11}{22} \) - \( \frac{12}{24} \) - \( \frac{13}{26} \) - ...and so on. **Negative Fractions:** Negative fractions can also be equivalent to \( \frac{1}{2} \) if both the numerator and denominator are negative: - \( \frac{-2}{-4} = \frac{1}{2} \) - \( \frac{-3}{-6} = \frac{1}{2} \) - \( \frac{-4}{-8} = \frac{1}{2} \) - ...and so forth. These examples demonstrate how different fractions can represent the same value as \( \frac{1}{2} \) by scaling the numerator and denominator proportionally.