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Inverse proportion

Two variables $$\Tblue{a}$$ and $$\Tgreen{b}$$ are inversely proportional if $$\Tblue{a}$$ is directly proportional to the reciprocal of $$\Tgreen{b}$$. We write $$\Tblue{a}\propto 1/\Tgreen{b}$$.

To cover a given distance, the time taken is inversely proportional to speed. The higher the speed, the shorter the time.

If $$\Tblue{a}$$ and $$\Tgreen{b}$$ are inversely proportional, their product is a constant $$\Tred{k}$$. $$\Tblue{a}\Tgreen{b}=\Tred{k},\qquad \Tblue{a} = \frac{\Tred{k}}{\Tgreen{b}}.$$

Several variables are collected in the table below. The variables $$\Tblue{a}$$ and $$\Tgreen{b}$$ are proportional with proportionality constant $$\Tred{10}$$. The variables $$\Tblue{a}$$ and $$\Tgreen{c}$$ are not proportional.

Variable $$\Tblue{a}$$ $$\Tblue{1}$$ $$\Tblue{2}$$ $$\Tblue{3}$$ $$\Tblue{4}$$ $$\Tblue{5}$$
Variable $$\Tgreen{b}$$ $$\Tgreen{10}$$ $$\Tgreen{5}$$ $$\Tgreen{3.33}$$ $$\Tgreen{2.5}$$ $$\Tgreen{2}$$
Product $$\Tred{a\times b}$$ $$\Tred{10}$$ $$\Tred{10}$$ $$\Tred{10}$$ $$\Tred{10}$$ $$\Tred{10}$$
Variable $$\Tgreen{c}$$ $$\Tgreen{10}$$ $$\Tgreen{25}$$ $$\Tgreen{11.11}$$ $$\Tgreen{6.25}$$ $$\Tgreen{4}$$
Product $$\Tred{a\times c}$$ $$\Tred{10}$$ $$\Tred{50}$$ $$\Tred{33.33}$$ $$\Tred{25}$$ $$\Tred{20}$$

From the table, we can deduce that the proportionality constant is $$\Tred{10}$$.