Question

which two ratios show a proportion a. 20/4 and 1/5 b. 20/4 and 2/5 c. 4/20 and 2/5 d. 4/20

Answer 1

To determine which two ratios show a proportion, we can use the property of cross-multiplication. Two ratios \( \frac{a}{b} \) and \( \frac{c}{d} \) are proportional if \( a \times d = b \times c \).

Let's evaluate each option:

a. \( \frac{20}{4} \) and \( \frac{1}{5} \)

Cross-multiply: \( 20 \times 5 = 100 \) and \( 4 \times 1 = 4 \)
- Not proportional since \( 100 \neq 4 \)

b. \( \frac{20}{4} \) and \( \frac{2}{5} \)

Cross-multiply: \( 20 \times 5 = 100 \) and \( 4 \times 2 = 8 \)
- Not proportional since \( 100 \neq 8 \)

c. \( \frac{4}{20} \) and \( \frac{2}{5} \)

Cross-multiply: \( 4 \times 5 = 20 \) and \( 20 \times 2 = 40 \)
- Not proportional since \( 20 \neq 40 \)

d. \( \frac{4}{20} \)

This option is a single ratio, not a pair to compare.

Given the options, none of the pairs of ratios in options a, b, or c show a proportion. If "d" were to compare with another ratio, we would need that context. However, based on your question's options, there seems to be no pair that shows a proportion.