To determine which pair of ratios are proportional, we can cross-multiply and see if the products are equal.
A. \( \frac{3}{4} \) and \( \frac{9}{14} \)
- Cross-multiplication: \( 3 \times 14 = 42 \) and \( 4 \times 9 = 36 \)
- \( 42 \neq 36 \) → Not proportional
B. \( \frac{1}{5} \) and \( \frac{3}{15} \)
- Cross-multiplication: \( 1 \times 15 = 15 \) and \( 5 \times 3 = 15 \)
- \( 15 = 15 \) → Proportional
C. \( \frac{6}{21} \) and \( \frac{2}{7} \)
- Cross-multiplication: \( 6 \times 7 = 42 \) and \( 21 \times 2 = 42 \)
- \( 42 = 42 \) → Proportional
D. \( \frac{19}{45} \) and \( \frac{6}{15} \)
- Cross-multiplication: \( 19 \times 15 = 285 \) and \( 45 \times 6 = 270 \)
- \( 285 \neq 270 \) → Not proportional
Thus, the pairs of ratios that are proportional are B (\( \frac{1}{5} \) and \( \frac{3}{15} \)) and C (\( \frac{6}{21} \) and \( \frac{2}{7} \)).