A unit rate is one in which the second number of the ratio is 1 - in some suitable units.
For example, 10 kilometres in 30 minutes can be converted to a unit rate as
20 kilometres per hour or 1/3 km per minute (or however many km per year, etc).
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If two ratios are equivalent then their cross-product must be 1, and their unit rates must be the same.
Rates are ratios ... Speed is a rate of distance per unit of time... ratio of distance to time. Proportions are two equal ratios, whether they are rates or not.
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By dividing