Unit rates with fractions

Calculate unit rates involving fractional quantities

Problem types

Dividing fractions
Finding a unit rate
Simplifying complex fractions · Useful idea
A rate with fractions of units, such as half a mile in a quarter hour, is a complex fraction.
Fraction operations on a line plot · Useful idea
A rate such as a fraction of a pound per person is a unit rate with fractions.
Converting within one measurement system · Useful idea
A rate such as miles per hour is converted by changing one unit at a time, and the unit rate may be a fraction.
Dividing with unit fractions · Useful idea
Dividing by a unit fraction counts how many such pieces fit, which gives rates such as miles per hour for a quarter of an hour.
Finding elapsed time · Useful idea
A speed in miles per hour divides a distance by elapsed time, so elapsed time of a fraction of an hour gives a fractional unit rate.

Linear models of a situation · Extend the idea
A unit rate with fractions is the slope of a linear model, such as miles per hour.
Slope of a line · See it applied
Slope is a unit rate: the change in vertical distance per one unit of horizontal change.
Average rate of change · Extend the idea
Average rate of change is a unit rate: change in output per one unit of input over an interval.

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