Ratio
A comparison of two numbers or quantities by division, such as 2 boys/5 boys
Rate
A comparison of two numbers or quantities (a ratio) measured with different units, such as 71 miles/3 gallons.
Unit rate
A rate in which the denominator is 1, such as 23 mi/gal
Proportion
An equation stating that two ratios are equal.
Changing from a rate to a unit rate
Divide the numerator (top) number by the denominator (bottom) number. The units remain the same.
Solve this proportion: 3/8 = 21/x
Cross-multiply: 3x = 8 � 21. Answer: x = 56
Is this a ratio or a rate? 16 horses/100 acres
Rate because the units are different. (Also a ratio because all rates are ratios.)
Write as a ratio: 50 minutes of practice in 1 hr 25 minutes
50 min/ 85 min (Reduces to 10/17) (Note: This is NOT a rate because the units are the same).
Writing Rates
are usually written using 'per', or a slash (/). Examples: miles per gallon or $/day.
Write as a unit rate: $2.69 for 54 paper plates
$0.05 per plate
Write as a unit rate: 12 pound turkey for $11.64
$0.97 per pound of turkey
Write as a unit rate: 10 pound ham for $18.89
$1.89 per pound
Write as a unit rate: $2.25 for 3 cans of Cranberries
$0.75 per can
Write as a unit rate: $1.99 for 5 pound bag of potatoes
$0.40 per pound
Write as a unit rate: $2.99 for 12 pack of Coke
$0.25 per can