Pre-Algebra · Ratios, rates and proportions

How to Find a Unit Rate

Problem

180\ \text{miles in}\ 3\ \text{hours}

Answer

60\ \text{miles per hour}

A unit rate tells you the amount for one unit, such as the price for one ticket or the distance in one hour. Divide the two amounts and keep the units.

Step-by-step solution

Write the rate as a fraction.
$\frac{180\ \text{miles}}{3\ \text{hours}}$
Why: A rate compares two amounts with different units.
Divide the top by the bottom.
$\frac{180}{3} = 60$
Why: The denominator becomes 1, so the rate is per one unit.
Write the unit rate with its units.
$60\ \text{miles per hour}$
Why: The units describe what one unit of the second amount gives.
Check the answer by multiplying back.
$60 \times 3 = 180$
Why: The check returns the original distance.

Common mistakes

Dividing hours by miles. The unit you want, such as speed, tells you which amount goes on top.
Using 180 times 3 instead of dividing.
Leaving the answer without units. A rate needs units.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

$240\ \text{miles in}\ 4\ \text{hours}$

Show answer

$60\ \text{miles per hour}$
$\$12\ \text{for}\ 3\ \text{kg}$

Show answer

$\$4\ \text{per kg}$
$96\ \text{words in}\ 8\ \text{minutes}$

Show answer

$12\ \text{words per minute}$
$\$45\ \text{for}\ 5\ \text{tickets}$

Show answer

$\$9\ \text{per ticket}$
$150\ \text{pages in}\ 5\ \text{days}$

Show answer

$30\ \text{pages per day}$