1. Section 3.1 Ratios and Rates

2. VOCABULARY
Ratio: a comparison of two quantities which can be written as:
a fraction - ¾, words – 3 to 4, or using a colon – 3:4.
Rate: a ratio of two quantities with different unit Ex miles
2 hours
Unit Rate: a rate with a denominator of 1 Ex. 55 miles
1 hour

3. Unit Analysis Unit Analysis is converting from one unit to another.
Example 1 – John works 6 hours at a rate of $12 per 1 hour.
How much money does John make working?
6 hours x $ = $72 Notice how the hours cancel out!
1 hour
Example 2 – Samantha’s car has 10 gallons of gas and gets 22 miles per 1 gallon.
How many miles can Samantha drive?
10 gallons x 22 miles = miles
1 gallon Notice how the gallons cancel out!
Example 3 – feet is how many miles?
11560 feet x 1 mile = = 2 miles
5280 feet Notice how the feet cancel out!
Example – How many seconds are in 13 minutes?
13 minutes x 60 seconds = seconds
1 minute Notice how the minutes cancel out!

4. Notice that the order you write the ratio has to match the order in
Finding Ratios, Rates, and Unit Rates
Example 1 – There are 14 girls and 17 boys in the class.
The ratio of girls to boys is: 14/17 or 14 to 17 or 14:17
The ratio of boys to girls is: 17/14 or 17 to 14 or 17:14
The ratio of boys to students in the class is: 17/31 or 17 to 31 or 17:31
Notice that the order you write the ratio has to match the order in
which it was asked.
Example 2 – John can run 400 yards in 10 seconds.
John runs at a rate of: 400 yards
10 seconds
The unit rate is how many yards John can run in one second.
400 yards ÷ 10 = 40 yards
10 seconds ÷ second
Example 3 – The cost of bananas is 99¢ for 3 pounds.
The rate is: ¢
3 pounds
The unit rate is how much does it cost for 1 pound.
99 ¢ ÷ 3 = ¢
3 pounds÷ pound

5. Finding a Rate From a Table
The table shows the distance the Internationals Space Station travels while
Orbiting the Earth. Find the speed in miles per second.
Time (seconds) 3 6 9 12
Distance (miles)
14.4
28.8
43.2
57.6
Find the change between intervals.
From the graph we can see that the Space Station travels 14.4 miles per 3 seconds.
Written as a rate that would be: miles
3 seconds
The unit rate (or speed in miles per 1 second) is: miles ÷ 3 = 4.8 miles
3 seconds ÷ second

6. Finding a Rate from a Line Graph
Sound through Water)
The graph shows the distance that sound travels
through water. Find the speed in kilometers per
second.
Step 1 – Choose a point on the line (2,3)
This point shows you that sound travels
3 kilometers in 2 seconds.
Step 2 – To find the speed in kilometers per second,
find the unit rate.
3 kilometers ÷ 2 = 1.5kilometers
2 seconds ÷ second
Distance (kilometers)
(2,3)
Time (seconds)