Question

which ratios form a proportion? \\(\frac{3}{4}\\) and \\(\frac{9}{16}\\) \\(\frac{1}{6}\\) and \\(\frac{3}{8}\\) \\(\frac{2}{3}\\) and \\(\frac{8}{12}\\) \\(\frac{2}{5}\\) and \\(\frac{5}{2}\\)

Explanation:

Step1: Recall proportion definition

A proportion is when two ratios are equal, i.e., \( \frac{a}{b}=\frac{c}{d} \) implies \( a\times d = b\times c \).

Step2: Check first pair \( \frac{3}{4} \) and \( \frac{9}{16} \)

Calculate cross - products: \( 3\times16 = 48 \), \( 4\times9 = 36 \). Since \( 48
eq36 \), not a proportion.

Step3: Check second pair \( \frac{1}{6} \) and \( \frac{3}{8} \)

Cross - products: \( 1\times8 = 8 \), \( 6\times3 = 18 \). \( 8
eq18 \), not a proportion.

Step4: Check third pair \( \frac{2}{3} \) and \( \frac{8}{12} \)

Cross - products: \( 2\times12 = 24 \), \( 3\times8 = 24 \). Since \( 24 = 24 \), they form a proportion.

Step5: Check fourth pair \( \frac{2}{5} \) and \( \frac{5}{2} \)

Cross - products: \( 2\times2 = 4 \), \( 5\times5 = 25 \). \( 4
eq25 \), not a proportion.

Answer:

The ratios \( \boldsymbol{\frac{2}{3}} \) and \( \boldsymbol{\frac{8}{12}} \) form a proportion.