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]


 

 

 

 

 

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