Determine whether the following numbers are in proportion or not $:$
$\frac{1}{3}, \frac{1}{4}, \frac{1}{6}, \frac{1}{7}$

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Solution

Step $1 :$ To check whether the given numbers are in proportion or not
As we know that any four numbers $a, b, c$ and $d$ are said to be in proportion if and only if
$\frac{a}{b} = \frac{c}{d}$
Step $2 :$ Given four numbers are $\frac{1}{3}, \frac{1}{4}, \frac{1}{6}, \frac{1}{7}$
Find the ratio of first and second number
$= \frac{\frac{1}{3}}{\frac{1}{4}}$
$= \frac{4}{3}$
Step $3 :$ Now find the ratio of third and fourth number
$= \frac{\frac{1}{6}}{\frac{1}{7}}$
$= \frac{7}{6}$
therefore the ratio of first term to second term is not equal to the ratio of third term to fourth term
$\frac{4}{3}$ $\neq \frac{7}{6}$
Hence, the given four numbers $\frac{1}{3}, \frac{1}{4}, \frac{1}{6}, \frac{1}{7}$ are not in proportion.

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