Question

1. which two quantities form a proportional relationship?

a $\frac{1}{4}$ and $\frac{3}{8}$

b $\frac{2}{15}$ and $\frac{3}{30}$

c $\frac{5}{6}$ and $\frac{5}{24}$

d $\frac{10}{18}$ and $\frac{45}{81}$

Explanation:

Step1: Test cross-multiplication for proportionality

For fractions $\frac{a}{b}$ and $\frac{c}{d}$, check if $a \times d = b \times c$.

Option A:

$\frac{1}{4}$ and $\frac{3}{8}$
$1 \times 8 = 8$, $4 \times 3 = 12$
$8
eq 12$, not proportional.

Option B:

$\frac{2}{15}$ and $\frac{3}{30}$
$2 \times 30 = 60$, $15 \times 3 = 45$
$60
eq 45$, not proportional.

Option C:

$\frac{5}{6}$ and $\frac{5}{24}$
$5 \times 24 = 120$, $6 \times 5 = 30$
$120
eq 30$, not proportional.

Option D:

$\frac{10}{18}$ and $\frac{45}{81}$
$10 \times 81 = 810$, $18 \times 45 = 810$
$810 = 810$, proportional.

Answer:

D. $\frac{10}{18}$ and $\frac{45}{81}$