## Unit rates and unit ratios

 A unit rate is a ratio that has a denominator of 1. A unit rate is also called a unit ratio. (They mean the same thing.) $\frac{5}{4}$ and $3:8$ and $40\mbox{ to }10$ are ratios, but they are not unit ratios. $\frac{1.25}{1}$ and $0.375:1$ and $4\mbox{ to }1$ are unit ratios. Any ratio can be converted into a unit ratio by dividing the numerator and the denominator by the denominator. $$\large~\frac{a}{b}=\frac{a÷b}{b÷b}=\frac{a÷b}{1}$$

Example 1

 At a school dance, there are 6 girls for every 3 boys. What is the ratio of girls to boy as a unit rate? (girls per boy) What is the ratio of boys to girl as a unit rate? (boys per girl) Example 2

 20 sticks of gum costs $1.25 What is the price per stick of gum?$\mbox{price:sticks}\,=\,1.25:20\,=\,\frac{1.25}{20}\,=\,\frac{1.25÷20}{20÷20}\,=\,\frac{0.0625}{1}$What is the ratio of sticks to price as a unit ratio?$\mbox{sticks:price}\,=\,20:1.25\,=\,\frac{20}{1.25}\,=\,\frac{20÷1.25}{1.25÷1.25}\,=\,\frac{16}{1}$# Self-Check Q1: Write the following ratio as a unit rate (km per hr): 474 km in 6 hours [show answer] Q2: Write the unit rate (cost per muffin).$2.00 for 5 muffins [show answer]

Q3: A 16-oz jar of peanut butter costs \$4.39. To the nearest cent, find the unit price in cents per ounce. [show answer]