Generate equivalent ratios

Equivalent ratios describe the same multiplicative relationship between two quantities: multiplying or dividing both terms of a ratio by the same positive nonzero factor preserves its value. Learners generate and justify equivalent ratios using ratio tables, double number lines, diagrams, or fraction notation, distinguishing this scaling relationship from adding the same amount to both terms; the focus is on positive quantities and proportional relationships rather than formal treatment of arbitrary or abstract ratio systems.

Detailed Explanation: Generate equivalent ratios

An equivalent ratio has the same relationship between its two quantities. To create one, multiply or divide both parts of the ratio by the same positive number.

Example

A recipe uses flour and sugar in a ratio of $3:5$ . Generate an equivalent ratio.

Start with the ratio:

3:5

Choose the same factor for both numbers. Let’s multiply by $4$ .
Multiply each part by $4$ :

3 \times 4 = 12

5 \times 4 = 20

Write the new ratio:

12:20

So, $3:5$ and $12:20$ are equivalent ratios.

You can justify this using fractions:

\frac{3}{5}=\frac{3\times4}{5\times4}=\frac{12}{20}

The relationship stays the same because both quantities were multiplied by the same factor. Adding the same number would not work: $3+4:5+4=7:9$ , which does not have the same value as $3:5$ .

Learn by doing: Generate equivalent ratios

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Ratios - Equivalent, Expanding Recipes with Non-Integer Multiples - Decimals

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