Ratios and Rates

Ratios and Rates

What is a ratio?

it compares 2 quantities using division 

 $\div$  

Example:  boys to girls, or circles to squares

What are rates?

When a ratio compares 2 quantities with unlike units, it is called a rate.

Examples: miles per gallon, cents per pound, dollars per movie ticket

Rates are ratios. What makes a ratio not a rate?

A ratio is not a rate if it compares 2 quantities of similar measurement.

Examples: teachers/students are similar

red counters/yellow counters are similar

Writing a ratio

The first quantity on top, the second quantity on the bottom in a

Example: A car travels 270 miles on 10 gallons of gas:

 $\frac{a}{b}$  form:   $\frac{270\ miles}{10\ gallons}$  

It is also a Rate because it is comparing unlike measurements

Let's put this in simplest form

 $\frac{270}{10}$  you will divide the numerator (top) by the denominator (bottom):  270  $\div$  10 gives us:   $\frac{27\ miles}{1\ gallon}$  

Our rate in simplest form is 27 miles per 1 gallon of gas

One more example

 $\frac{3\ chaperones}{15\ students}$  

there are 3 chaperones for every 15 students


This is not a rate because it compares similar units of measurement.  In simplest form (by dividing numerator by the denominator) is  $\frac{1\ chaperone}{5\ students}$ 

Multiple Choice

What is the ratio for: apples cost $4 for 2 pounds

• $\frac{1\ pound}{4\ dollars}$

• $3$

• $\frac{4\ dollars}{2\ pounds}$

Poll

What is the ratio for 48 miles in 3 hours?

• $\frac{48}{3}$

• $12$

Multiple Select

Is the ratio 625 visitors in 5 hours a rate?

• yes

• no

Multiple Choice

What is the ratio

 $\frac{40}{5}$  in simplest form?

• 2

•  $\frac{8}{1}$  

Poll

Do you understand ratios and rates?

• yes

• no

• getting there