1. Bell Work Write the ratio in simplest form: 18 24
Write the above simplified ratio two other ways.
In Max’s class there is a ratio of 3 girls to 4 boys. If there are 21 girls in his class how many boys are there? 3 4
3 to 4 and 3:4

2. Remember? A Ratio is a comparison of two quantities.
Unit Rates
Remember? A Ratio is a comparison of two quantities.
A ratio that compares two quantities with different kinds of units is called a rate.
A UNIT RATE is when a rate has been simplified so that it has denominator of 1.

3. For example… 15 mi 1 hr = 15 mi/h = 15 miles per hour
This is an example of a ratio that is also a rate:
30 𝑚𝑖𝑙𝑒𝑠 2 ℎ𝑜𝑢𝑟𝑠
The unit rate for: 30 𝑚𝑖𝑙𝑒𝑠 2 ℎ𝑜𝑢𝑟𝑠 = 30 𝑚𝑖𝑙𝑒𝑠 2 ℎ𝑜𝑢𝑟𝑠
15 mi
1 hr =
15 mi/h =
15 miles per hour

4. Rate Unit Rate Name The table below shows some common unit rates
“you don’t have to write this down”
Rate
Unit Rate
Name
miles per hour
Average speed
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑖𝑙𝑒𝑠 1 ℎ𝑜𝑢𝑟
miles per gallon
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑖𝑙𝑒𝑠 1 𝑔𝑎𝑙𝑙𝑜𝑛
Gas mileage
price per pound
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 1 𝑝𝑜𝑢𝑛𝑑
Unit price

5. Example 1
Adrienne biked 24 miles in 4 hours. If she biked at a constant speed, how many miles did she ride in one hour?
Step 1: Write the rate as a fraction:
Step 2: Divide the numerator and the denominator by ____________: 4
Step 3: Simplify!
Answer: Adrienne biked 6 miles in one hour

6. Find each unit rate. Round to the nearest hundredth if necessary.
$300 for 6 hours
220 miles on 8 gallons
18 cans for $6
Julia read 51 pages in 2 hours. What is the average number of pages she read per hour?
$300 6 ℎ𝑜𝑢𝑟𝑠 = $50 1 ℎ𝑜𝑢𝑟 = $50 per hour
220 𝑚𝑖𝑙𝑒𝑠 8 𝑔𝑎𝑙𝑙𝑜𝑛𝑠 = 27.5 𝑚𝑖𝑙𝑒𝑠 1 𝑔𝑎𝑙𝑙𝑜𝑛 =27.5 𝑚𝑖𝑙𝑒𝑠 𝑝𝑒𝑟 𝑔𝑎𝑙𝑙𝑜𝑛
18 𝑐𝑎𝑛𝑠 $6 = 3 𝑐𝑎𝑛𝑠 $1 =3 𝑐𝑎𝑛𝑠 𝑝𝑒𝑟 𝑑𝑜𝑙𝑙𝑎𝑟
51 𝑝𝑎𝑔𝑒𝑠 2 ℎ𝑜𝑢𝑟𝑠 = 25.5 𝑝𝑎𝑔𝑒𝑠 1 ℎ𝑜𝑢𝑟 =25.5 𝑝𝑎𝑔𝑒𝑠 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟

7. $2 for eight juice boxes = $2 8 𝑏𝑜𝑥𝑒𝑠
Find the unit price if it costs $2 for eight juice boxes
$2 for eight juice boxes = $2 8 𝑏𝑜𝑥𝑒𝑠
Step 1: right the rate as a fraction.
Step 2 Divide the numerate and the denominator by 8.
Step 3: Simplify.
$ ÷8 8 𝑏𝑜𝑥𝑒𝑠÷8
= $ 𝑏𝑜𝑥 =$0.25 𝑝𝑒𝑟 𝑏𝑜𝑥

8. What is the better buy?
The price of 3 different bags of dog are given in the table. Which size bag has the lowest price per pound rounded to the nearest cent?
Bag size (lb)
Price ($) 40
49.00 20
23.44 8
9.88
≈$1.23 𝑝𝑒𝑟 𝑝𝑜𝑢𝑛𝑑
≈$1.17 𝑝𝑒𝑟 𝑝𝑜𝑢𝑛𝑑
≈$1.24 𝑝𝑒𝑟 𝑝𝑜𝑢𝑛𝑑
𝑇ℎ𝑒 20 𝑝𝑜𝑢𝑛𝑑 𝑏𝑎𝑔 𝑠𝑒𝑙𝑙𝑠 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑙𝑜𝑤𝑒𝑠𝑡 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑝𝑜𝑢𝑛𝑑.

9. A store sells the same pasta the following two ways:
10 pounds of bulk pasta for $15.00
2 pounds of packaged pasta for $3.98
Bulk Pasta: $15.00= $1.50
10 lb lb
Packaged Pasta:
$3.98 = $1.99
2 lb lb
Which is the better buy? Find the unit price for both types.
The bulk pasta is the better buy because it costs less per pound.

10. What is best? $4.00 / 10 = $0.40 per pencil or 6 pencils for $2.70 ?
Here is the Unit Cost:
$4.00 / 10 = $0.40 per pencil
$2.70 / 6 = $0.45 per pencil
So the lowest Unit Price (and the best bargain) is 10 pencils for $4.00

11. In this case the "Unit" is 1 liter, and the Unit Prices are:
Comparing
Comparing Unit Prices can be a good way of finding which is the "best buy".
Example: What is best?
2 liters of Milk at $3.80, or
1.5 liters of Milk at $2.70 ?
In this case the "Unit" is 1 liter, and the Unit Prices are:
$3.80 / 2 liters = $1.90 per liter
$2.70 / 1.5 liters = $1.80 per liter
So the lowest Unit Price (and the best bargain) is 1.5 liters at $2.70.

12. You buy a package of 6 pairs of athletic socks for $8. 94
You buy a package of 6 pairs of athletic socks for $ Write this as a unit rate.
$1.49 per pair
A bullet train in Japan can travel 186 miles in 2 hours. Write this as a unit rate.
93 mi/h
Which is the better buy?
Cereal: 17 ounces for $3.40 or
14 ounces for $3.08
17 ounces for $3.40