Simple proportion

Japanese school year: Elementary 5

What you learn

Learn the relationship where one quantity doubles or triples as the other quantity doubles or triples. This concept is useful in daily life, such as calculating total costs based on quantities purchased. Prior knowledge of basic changing quantities and multiplication is essential.

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Key points

This formula expresses a direct proportion where $y$ is proportional to $x$ . When $x$ doubles or triples, $y$ also doubles or triples; multiplying the constant $k$ by $x$ gives the value of $y$ .

y = k \times x

This formula is used to find the constant multiplier $k$ (constant of proportionality) in a direct proportion. Dividing any $y$ by its corresponding $x$ always produces the exact same value $k$ .

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

This formula is used to solve for an unknown value in a direct proportion. It relies on the property that the ratio of $y$ to $x$ remains strictly equal across any corresponding pairs.

\frac{y_1}{x_1} = \frac{y_2}{x_2}

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Practice 1Coming soon