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Calculate unit rates

Unit-rate understanding involves finding the amount of one quantity corresponding to exactly one unit of another by dividing the quantities, including ratios involving whole numbers, decimals, or fractions. The resulting rate is interpreted with its units, such as miles per hour or dollars per item, and equivalent unit rates in tables, equations, and graphs are recognized as representing the same relationship; reversing the quantities produces a different rate. More advanced treatments, such as instantaneous rates and formal function analysis, are not included.

Detailed Explanation: Calculate unit rates

A unit rate tells how much of one quantity corresponds to exactly 1 unit of another quantity.

To find a unit rate:

  1. Identify the two quantities and their units.
  2. Divide the first quantity by the second quantity.
  3. Write the answer with units.
  4. Check that the denominator is 11.

Example: A car travels 156156 miles in 33 hours. What is its speed in miles per hour?

Write the rate as a fraction:

156 miles3 hours\frac{156\text{ miles}}{3\text{ hours}}

Divide both quantities by 33:

156 miles3 hours=52 miles1 hour\frac{156\text{ miles}}{3\text{ hours}}=\frac{52\text{ miles}}{1\text{ hour}}

So, the unit rate is:

52 miles per hour\boxed{52\text{ miles per hour}}

This means the car travels 5252 miles in 11 hour. Be careful about the order: dividing hours by miles would give a different rate, such as hours per mile.

Learn by doing: Calculate unit rates

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    Ratios - Unit Rates, Solve for Rate

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