Question

Make set of all possible proportions from the numbers $15,18,35\text{and}42.$

Answer 1

Given, numbers are $15,18,35\text{and}42$.
Then, the possible proportions are as follows:

$15:18=35:42$
$15:18=\frac{15}{18}=\frac{7\times 5}{7\times 6}=\frac{5}{6}$
$\text{and}$

$35:18=\frac{35}{18}=\frac{7\times 5}{7\times 6}=\frac{5}{6}$

$\therefore$ $\text{Ratio}15:18=\text{Ratio}35:42$

Hence, they form a proportion.


$15:35=18:42$

$15:35=\frac{15}{35}=\frac{3\times 5}{7\times 5}=\frac{3}{7}$,
$\text{and}$

$18:42=\frac{18}{42}=\frac{6\times 6}{7\times 6}=\frac{3}{7}$

$\therefore$ $\text{Ratio}15:35=\text{Ratio}18:42$

Hence, they form a proportion .

$42:18=35:15$

$42:18=\frac{42}{18}=\frac{7\times 6}{3\times 6}=\frac{7}{3}$,
$\text{and}$

$35:15=\frac{35}{15}=\frac{7\times 5}{3\times 5}=\frac{7}{3}$

$\therefore$ $\text{Ratio}42:18=\text{Ratio}35:15$

Hence, they form a proportion .


$42:35=18:15$

$42:35=\frac{42}{35}=\frac{7\times 6}{7\times 5}=\frac{6}{5}$,
$\text{and}$

$18:15=\frac{18}{15}=\frac{3\times 6}{3\times 5}=\frac{6}{5}$

$\therefore$ $\text{Ratio}42:35=\text{Ratio}18:15$

Hence, they form a proportion .