Unit rates and unit prices

750 grams for 4.80 is cheaper per gram than 500 grams for 3.40, even though the bigger pack costs more.

Two bags of rice on a shelf

Picture two bags of rice on a shop shelf. One holds 500 grams for 3.40 dollars, the other 750 grams for 4.80. The bigger bag costs more, so is the smaller one the bargain? Not here. The answer comes from turning each price into a price for the same amount of rice. That step has a name, and it is the subject of this page: a unit rate.

Kilometres per hour, dollars per gram

A ratio compares quantities with the same unit. Very often we want to compare quantities with different units: kilometres and hours, dollars and grams, words and minutes. OpenStax calls this a rate: a comparison of two quantities of different units, usually written as a fraction with the units kept in it. 300 kilometres in 4 hours is the rate 300 km / 4 h.

300 km in 4 hours becomes 75 km in one

A unit rate is a rate whose denominator is 1 unit. To get one, divide the numerator by the denominator. 300 km in 4 hours is 300 ÷ 4 = 75 km per 1 hour, written 75 km/h. Hourly pay is a unit rate too: 384 dollars for 32 hours of work is 384 ÷ 32 = 12 dollars per hour. Unit rates are useful because they are ready to multiply. At 75 km/h, 3 hours covers 3 × 75 = 225 km.

The lower price per egg wins

A unit price is a unit rate that gives the price of one item, or of one unit of weight or volume. Twelve eggs for 3.60 dollars is 3.60 ÷ 12 = 0.30 dollars an egg. OpenStax notes that the better buy is the item with the lower unit price, and that most grocery stores list the unit price on the shelf. South Korea writes this into a government notice, the Price Display Guidelines, which lists the goods that must show a unit price. An April 2025 revision raised that list from 84 to 114 kinds of goods and allowed some exceptions to the unit: foil is priced per metre, but sheet-type paper foil may be priced per sheet.

Compare a 500-gram bag of rice for 3.40 dollars with a 750-gram bag for 4.80 dollars. Per gram: 3.40 ÷ 500 = 0.0068 and 4.80 ÷ 750 = 0.0064. The numbers are small, so shelf labels often use 100 grams as the unit instead: 0.68 dollars per 100 g against 0.64 dollars per 100 g. The bigger bag is the better buy, by 4 cents per 100 grams. Bigger is often cheaper per unit, but not always, which is the reason to check.

Minutes per kilometre or kilometres per minute?

Every rate can be flipped. A runner covers 10 km in 50 minutes: that is 10 ÷ 50 = 0.2 km per minute, or 50 ÷ 10 = 5 minutes per kilometre. Both are correct unit rates. Choose the one whose "per" unit matches the question. "How far in 30 minutes?" wants km per minute: 0.2 × 30 = 6 km. "How long for 7 km?" wants minutes per km: 5 × 7 = 35 minutes.

Words such as per, in, for and on signal a rate. OpenStax gives a short test: if the two units measure the same kind of quantity, you have a ratio; if they are different, you have a rate. Either way you write a fraction.