1. Chapter 7-1 Ratios and Rates
Unit 3
Chapter 7-1 Ratios and Rates

2. Ratios A ratio is a comparison of two numbers or quantities.
If a gallon of orange juice contains 3 parts oranges and 2 parts sugar, then the ratio comparing the oranges and sugar can be written as follows:
3 to :
Remember that a fraction bar represents division. When the first number being compared is less than the second, the ratio is usually written as a fraction in simplest form.
2 6 = 1 3
GCF is of 2 and 6 is 3

3. Examples
Example 1: Express the ratio 9 cards out of 18 cards in the deck as a fraction in simplest form. 9÷9 18 ÷9 = 1 2 [divide numerator and denominator by the GCF 9]
Example 2:
NOTE: When writing a ratio involving measurements, both quantities should have the same unit of measure.
Express the ratio 2 feet to 16 inches as a fraction in simplest form
2 𝑓𝑒𝑒𝑡 16 𝑖𝑛𝑐ℎ𝑒𝑠 = 24 𝑖𝑛𝑐ℎ𝑒𝑠 16 𝑖𝑛𝑐ℎ𝑒𝑠 [convert 2 feet to inches]
= 3 𝑖𝑛𝑐ℎ𝑒𝑠 2 𝑖𝑛𝑐ℎ𝑒𝑠 [Divide numerator and denominator by GCF 8]
Written in simplest form, the ratio is 3 to 2

4. Rate vs Unit Rate
A rate is a ratio of two measurements having different kinds of units.
For example: 70 miles in 5 hours miles and hours are different units
$20 for 3 pounds dollars and pounds are different units
When a rate is simplified so that it has a denominator of 1, it is called a unit rate.
An example of unit rate would be $5 per pound, which means $5 per 1 pound

5. Find Unit Rate Example:
A package of 20 crayons costs $18 and a package of 30 crayons costs $28. Which package has the lower cost per crayon?
Find and compare the unit rate of the packages
18 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 20 𝑐𝑟𝑎𝑦𝑜𝑛𝑠 = .9 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 1 𝑐𝑟𝑎𝑦𝑜𝑛 divide numerator and denominator by 20 to get a denominator of 1
= For the 20 pack, the unit rate is $0.90 per crayon
28 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 30 𝑐𝑟𝑎𝑦𝑜𝑛𝑠 = .93 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 1 𝑐𝑟𝑎𝑦𝑜𝑛 divide numerator and denominator by 30 to get a denominator of 1
= For the 30 pack, the unit rate is $0.93 per crayon
So the package with the 20 crayons has the lower cost per crayon.

6. Let’s practice! Write each ratio as a fraction in simplest form
1) 4 weeks to plan 2 vacations 2) 3 days to take 2 tests
Express each ratio as a unit rate
3) $3.50 for 5 drinks 4) $56 for 6 tickets
5) $3.99 for 3 gallons of gas

7. Let’s Check Our Answers!
Write each ratio as a fraction in simplest form
1) 4 weeks to plan 2 vacations 2) 3 days to take 2 tests
4 2 =
Express each ratio as a unit rate
3) $3.50 for 5 drinks 4) $56 for 6 tickets
= $0.70 for 1 drink = $7 for 1 ticket
5) $3.99 for 3 gallons of gas
= $1.33 per 1 gallon