unit rate
When you see “60 dollars for 4 hours of work,” it is hard to compare with “75 dollars for 5 hours.” A unit rate fixes this by reducing the second quantity to exactly one: how much per single hour, per single item, per single mile. Both jobs above pay 15 dollars per hour, so they are equally good.
A rate compares two quantities with different units, such as kilometers and hours, and is read as a kind of ratio. A unit rate is a rate whose second quantity has been scaled down to 1, found by dividing the first quantity by the second. So 150 kilometers in 3 hours becomes 150 ÷ 3 = 50 kilometers per hour.
Unit rates are the everyday tool of comparison shopping and of speed, density, and price. They convert a tangled comparison into a single number with a clear “per one” meaning. The unit price on a store shelf — dollars per liter, cents per gram — is a unit rate placed there precisely so you can compare unequal package sizes at a glance.
Which is cheaper: 12 eggs for 4.20 dollars, or 18 eggs for 6.12 dollars? Unit prices are 4.20 ÷ 12 = 0.35 and 6.12 ÷ 18 = 0.34 per egg, so the 18-pack wins.
Divide to put each price on a per-egg basis, then the smaller number is the better deal.
A unit rate is closely tied to slope: when two quantities vary together at a constant unit rate, plotting them gives a straight line through the origin, and the unit rate is exactly that line's slope.