Ratios and Rates
Chapter 5 Section 1
What is a ratio?
• Ratio: a comparison of two quantities by
division.
• Can be written in 3 ways:
5 to 26
5:26
5
25
Writing ratios: Two ways
1) Part to part:
– Black keys to white
keys:
Writing ratios: Two ways
2) Part to whole:
– Black keys to all
keys
Writing ratios as
decimals
• An official U.S. flag has a length-to-width
ratio of 19:10. The largest U.S. flag
measures 505ft by 255 ft. Is this an
official U.S. flag?
Simplifying Ratios
• Same as simplifying fractions.
• A black bear weighs about 325lb. A
polar bear weighs about 1,000lb. Write a
ratio in simplest form to compare the
weights of the bears.
325 ÷25
1000 ÷25
=
13
40
Simplify
105
•
1350
240
•
402
Finding Unit Rates
• Vocabulary:
– Rate: a ratio that compares two quantities
measured in different units.
• Ex 1: 233 words in two minutes
• Ex 2: 100 miles in 2 hours
– Unit Rate: a rate for one unit of a given
quantity.
• Ex 1: 50 miles per hour (one hour)
• Ex 2: 115 feet per minute (one minute)
Finding Unit Rate
Rate:
150 heartbeats
2 minutes
Unit Rate (Divide to get it):
150 ÷ 2 = 75 heartbeats per minute.
Find the Unit Rate
Amy can read 88 pages in 4 hours. What is the
unit rate? (How many pages can she read per
hour?)
88 pages
4 hours
Find the Unit Rate
John drives 195 miles in 5 hours. What is the
unit rate?
195 miles
5 hours
Find the Unit Rate
Brandon can walk 1,200 feet in 300 seconds.
What is the unit rate?
Using Unit Prices
• Unit price: cost per item.
– Example: a box of cereal weighs 8 oz and
has a unit price of $0.31 per ounce. You
want to know the total price of the box of
cereal. How?
Another Example
• The unit price for dog food is $0.35/lb.
How much does a 20-lb bag of dog food
cost?
Another Example
• The unit price for dog food is $0.35/lb.
How much does a 20-lb bag of dog food
cost?
• EXTENSION:
– If the price drops to $0.32/lb, what is the
difference in price for the 20lb bag?
Using Unit Rates to
Compare Prices
• Miss Yates’ is buying a bag of candy for
the class. A bag of 100 suckers costs
$21.99 on Amazon. A bag of 75 suckers
costs $18.99 at Walmart. Which place
has the better buy?
Another Example
• You are shopping for shampoo. The 16
oz bottle costs $6.19 and the 13.5 oz
bottle costs $3.99. Which size is the
better buy? Round to the nearest cent.
Try on your own.
• 48 fl oz of fruit juice costs $3.05 and 64 fl
oz costs $3.59. Which one is the better
buy?
Homework
• Pg. 245 #’s 1 – 16