Converting Rates
Calculate and apply Converting Rates in Grade 9 math. Solve real-world problems involving ratios, rates, and percent change with step-by-step guidance.
Key Concepts
Property Set up the conversion factor so the units of measure cancel.
Examples Convert 45 miles per hour to miles per minute: $\frac{45 \text{ miles}}{1 \text{ hour}} \cdot \frac{1 \text{ hour}}{60 \text{ minutes}} = \frac{45 \text{ miles}}{60 \text{ minutes}} = 0.75$ miles per minute. Convert 2 gallons per minute to quarts per minute: $\frac{2 \text{ gallons}}{1 \text{ minute}} \cdot \frac{4 \text{ quarts}}{1 \text{ gallon}} = \frac{8 \text{ quarts}}{1 \text{ minute}}$.
Explanation Need to switch from miles per hour to feet per second? That's converting rates! The trick is multiplying by a special fraction, called a conversion factor, that equals one, like $\frac{60 \text{ seconds}}{1 \text{ minute}}$. You cleverly arrange it so the old units on top and bottom cancel out, leaving you with the brand new units you want.
Common Questions
How do you convert a rate using dimensional analysis?
Multiply by a conversion factor (a fraction equal to 1) so the unwanted units cancel. Keep track of units at each step and simplify.
What is the difference between a unit rate and a rate?
A rate compares two quantities with different units. A unit rate is a rate where the denominator is 1, such as 60 miles per 1 hour.
How do you convert miles per hour to feet per second?
Multiply by (5280 feet / 1 mile) and (1 hour / 3600 seconds). The miles and hours cancel, leaving feet per second.