Rate and unit rate
Ninety boxes pass in six minutes. What one number says how fast the belt runs, and how do you use it to compare, predict and convert?
Where you are 5 inside
What this area is about
A rate is a ratio of two amounts measured in different units: boxes and minutes, dollars and liters, miles and hours. Its unit rate is how much of the first amount goes with exactly one of the second, found by division: 90 boxes in 6 minutes is 90 \div 6 = 15 boxes per minute. One number like that answers questions about any amount.
How these fit together
The definition. Rates and unit rates says what a rate is and how to scale one to “per one”.
Familiar rates. Speed, distance and time is distance per unit of time; at a constant speed it gives how far something goes or how long it takes. Unit price and comparing rates is price per item or per unit of measure, used to decide which package size gives more for the money.
Procedures. Unit rates when the amounts are fractions finds the amount per one when both amounts are fractions. Changing the units of a rate rewrites a rate, such as feet per minute as miles per hour, by multiplying by conversion factors equal to 1, so the rate itself does not change.
A path through it
Rates and unit rates come first. The other four each build on it and can follow in any order. Unit price also uses comparing two ratios, and changing units uses converting customary units.
Finish here and the constant of proportionality, rate of change, density and conversion factors build on it.