Question

If $m\propto \frac{1}{n}$, complete the following table:

$m$	$12$	.....	$6$	.....
$n$	$10$	$4$	.....	$8$

Answer 1

$m$	$12$	$30$	$6$	$15$
$n$	$10$	$4$	$20$	$8$

Given proportion is $m\propto \frac{1}{n}$
$\therefore m=k\frac{1}{n}$ (where $k$ is a constant of variation)
$\therefore k=mn$ ...(1)
Substituting $m=12$ and $n=10$ in equation (1), we get
$k=12\times 10=120$

(a) When $n=4$, $k=120$, $m=$?
$\Rightarrow m=\frac{k}{n}=\frac{120}{4}=30$

(b) When $m=6$, $k=120$, $n=$?
$\Rightarrow n=\frac{k}{m}=\frac{120}{6}=20$

(c) When $n=8$, $k=120$, $m=$?
$\Rightarrow m=\frac{k}{n}=\frac{120}{8}=15$