Finding an Equivalent Rate
Finding an equivalent rate is a Grade 8 skill in Saxon Math Course 3 where students scale a rate up or down to create proportionally equal rates for comparison or problem solving. By multiplying or dividing both parts of a rate by the same number, students produce equivalent rates that preserve the original relationship. This skill is fundamental to solving proportion and unit rate problems in math and science.
Key Concepts
Property To convert a rate like miles per minute to miles per hour, multiply by a unit multiplier that cancels the original time unit: $\frac{1 \text{ mile}}{5 \text{ min}} \cdot \frac{60 \text{ min}}{1 \text{ hr}} = \frac{12 \text{ mi}}{1 \text{ hr}}$.
Examples A snail crawls 2 feet per minute. Find its speed in feet per hour: $\frac{2 \text{ ft}}{1 \text{ min}} \times \frac{60 \text{ min}}{1 \text{ hr}} = \frac{120 \text{ ft}}{1 \text{ hr}}$ Convert 440 yards per minute to yards per second: $\frac{440 \text{ yd}}{1 \text{ min}} \times \frac{1 \text{ min}}{60 \text{ sec}} = \frac{7.33 \text{ yd}}{1 \text{ sec}}$.
Explanation So, you ran a mile in 5 minutes and want to brag about your speed in miles per hour? No problem! Just multiply your rate by the unit multiplier $\frac{60 \text{ min}}{1 \text{ hr}}$. The 'minutes' cancel out, leaving you with your awesome new speed to share.
Common Questions
What is an equivalent rate in math?
An equivalent rate is a rate that represents the same relationship as the original but uses different numbers. For example, 60 miles/2 hours and 30 miles/1 hour are equivalent rates.
How do you find an equivalent rate?
Multiply or divide both the numerator and denominator of the rate by the same non-zero number. This preserves the ratio while changing the values.
How are equivalent rates used in Saxon Math Course 3?
Saxon Math Course 3 uses equivalent rates to compare two rates with different units, convert rates to unit rates, and set up proportions for problem solving.
What is the difference between a rate and a unit rate?
A rate compares two quantities with different units. A unit rate has a denominator of 1, making it easier to compare. Finding the unit rate requires dividing both parts of the rate by the denominator.
How do equivalent rates relate to proportions?
Two equivalent rates form a proportion. Setting two rates equal to each other creates a proportion equation that can be solved by cross-multiplication.