Direct & inverse proportion

Japanese school year: Elementary 6

What you learn

Learn the properties, formulas, and graphs of direct and inverse proportion, where ratios or products remain constant. These relationships are widely used to model quantitative phenomena in science and economics. Prior understanding of expressions with variables and fractions or decimals is helpful.

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Key points

This formula represents a direct proportion where $y$ is proportional to $x$ . Multiplying the independent variable $x$ by the constant $a$ (constant of proportionality) yields $y$ .

y = ax

This formula is used to determine the constant of proportionality $a$ in a direct proportion. Dividing any value of $y$ by its corresponding $x$ always yields the same constant $a$ .

\frac{y}{x} = a \quad (x \neq 0)

This formula represents an inverse proportion where $y$ is inversely proportional to $x$ . Dividing the constant $a$ by $x$ gives $y$ ; as $x$ doubles or triples, $y$ becomes $\frac{1}{2}$ or $\frac{1}{3}$ of its value.

y = \frac{a}{x} \quad (x \neq 0)

This formula is used to find the constant $a$ in an inverse proportion. Multiplying any corresponding pair of $x$ and y always yields the exact same product $a$ .

xy = a

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Practice 1Coming soon