### Ratios and rates

```Ratios
February, 2011

A ___________ is a comparison of two numbers by
division.

A ratio must be expressed in __________ .

Example #1:
There are approximately 600 students at Lewisburg
School. There are 30 teachers. What is the student to
teacher ratio at Lewisburg School?
600/30 or 20/1
3 ways to write a RATIO!


There were 6 chocolate donuts in the box of 12
donuts.
6
Part to Whole = 12
1
= 2
** This can be expressed as: **
1
1:2
1 to 2
2
ALL THREE OF THESE MEAN ~
1 CHOCOLATE DONUT FOR EVERY 2 DONUTS.
Equivalent Ratios

Two ratios are the same when put in simplest form.

Example – Are these two ratios equivalent?:

\$4 for every 16 ounces
\$4/16 oz =

\$10 for every 40 ounces
\$10/40 oz =

These two ratios are equivalent!!
Choose a partner and take turns taking each others pulse for
2 minutes.
1. Count the number of beats for each of you.
2. Write the ratio beats to minutes as a fraction.
1st block

A ___________ is a ratio that compares two different
kinds of units.

Example:
Heartbeat example


Two Units = heartbeats and minutes

A ____________ is a ratio that is simplified so that it has
a denominator of ONE unit.

Examples:
1. I made \$300 for 6 hours of work. Write the unit rate.
300/6 = 50/1
2.
We drove 220 miles on 8 gallons of gas. Write the unit
rate
220/8 = 27.5/1
How to calculate unit rate?

Easiest way is to divide BOTH the numerator AND the
denominator by the denominator.

Example #1:
\$ 15
3 pounds

15  3
33

\$5
1 pound
How to calculate unit rate?

Easiest way is to divide BOTH the numerator AND the
denominator by the denominator.

Example #2:
220 heartbeats
4 min utes

220  4
44

55 heartbeats
1 min ute
Common Unit Rates
Rate
Unit Rate
Common Unit Rates
Rate
Unit Rate
Number of Miles
1 hour
Miles per hour
Number of Miles
1 gallon
Miles per gallon
Number of Dollars
Price per pound
1 pound
Number of Dollars
1 hour
Dollars per
hour
Different Types of Ratios
Different Types of Ratios
Ratios
Comparing
Same
Measures
Part/Whole
(Fraction)
Comparing
Different Type
of Measures
Part/Part
Rate
Different Types of Ratios
Part/Whole
Examples
Ratio
Part/Part
Examples
Ratio
Rate Examples
Number of red roses
to number of flowers
in bouquet
Number of red
roses to number
of yellow roses
Number of roses per
bouquet
Number of footballs
to number of balls in
gym supply
Number of
footballs to
number of soccer
balls
Number of footballs
per class
Number of points
earned to number of
points possible
Number of points
earned to the
number of points
not earned
Number of points
earned per pupil
Number of girls to
number of student in
class
Number of girls
to number of
boys in class
Number of students
per teacher
Rate
Different Types of Ratios
Part/Whole
Examples
Ratio
Part/Part
Examples
Ratio
Rate Examples
Rate
Number of red roses
to number of flowers
in bouquet
6/24
Number of red
roses to number
of yellow roses
6 to 18
Number of roses
per bouquet
12:1
Number of footballs
to number of balls in
gym supply
5/25
Number of
footballs to
number of soccer
balls
5 to 8
Number of
footballs per class
5:5
Number of points
earned to number of
points possible
80/100
Number of points 80 to 20
earned to the
number of points
not earned
Number of points
earned per pupil
1140:15
or
76:1
Number of girls to
number of student in
class
14/22
Number of girls
to number of
boys in class
Number of
students per
teacher
22:1
14 to 8
Grocery Store Comparison – UNIT RATE!
Four
Products:
Find
the best price!!
Let’s try together:
http://math.rice.edu/~lanius/proportions/rate.html
Practice

Small Group:
 Number your paper from 1-12
 Deck of cards
 LEVEL 0: INDIVIDUAL
 Deal
out cards evenly to each player
 Rotate the card (clockwise) to your partner
 Continue until you’ve answered all cards

LEVEL 1: PARTNERS
 Check