Unit rate

Finding one

Divide by the quantity you want one of:

$$\frac{150 \text{ miles}}{3 \text{ hours}} = 50 \text{ miles per hour}$$ $$\frac{3 \text{ dollars}}{4 \text{ apples}} = 0.75 \text{ dollars per apple}$$

The unit you want one of goes on the bottom. Turning the division around gives a different — and equally valid — rate: $1.33$ apples per dollar.

Why one is the useful number

Two bags of rice: $5$ pounds for $8$ dollars, or $12$ pounds for $18$. Neither price nor weight settles which is cheaper, because both differ at once.

$$\frac{8}{5} = 1.60 \text{ per pound} \qquad \frac{18}{12} = 1.50 \text{ per pound}$$

Reduced to the same $1$, the comparison becomes a single subtraction. This is why speeds, wages, fuel economy and shelf prices are all quoted per one — see unit rates for the full method.

The same number under other names

Context	Name
shopping	unit price
a proportional equation $y = kx$	constant of proportionality
a straight-line graph	slope

These are one idea seen from three directions: how much $y$ changes for one step of $x$.