1. Ratios, Rates, and Unit Rates
Section 6.1 and 6.2

2. Notes
A ________________ is a comparison of two quantities by division.
If the first number being compared is less than the second, the ratio us usually written as a fraction in __________ form.
Ratios can express _________ to __________, __________ to __________, or ________ to ___________ relationships.

3. Key Concept: Ratios Words
A ratio is a comparison of two quantities by division
Examples
Numbers
Algebra
3 to 9
3:9
3/9
a to b
a:b
a/b

4. Compare and Contrast: Ratios and Rates

5. Examples
1.Ten out of every 30 Americans own a portable MP3 player. Express this ratio as a fraction in simplest form. Explain its meaning.
2. 15 out of 100 campsites at a campground are reserved for campers with pets. Express this ratio as a fraction in simplest form. Explain its meaning.

6. Notes Simplify Ratios Involving Measurements
When writing a ratio involving measurements, both quantities should have the same measure.
Example:
1. Express the ratio 8 ounces to 3 pounds as a fraction in simplest form.
2. Express the ratio 15 inches to 1 foot as a fraction in simplest form.

7. On your Own Express each ratio as a fraction in simplest form.
1. 12 boys to 16 girls
2. 24 out of 60 light bulbs

8. On your Own 3. 10 yards to 10 feet 4. 6 feet to 14 inches
5. 4 players to 52 cards

9. Notes
A __________ is a ratio of two quantities having different kinds of units.
Example: 60 characters in 30 seconds
When a rate is simplified so that it has a denominator of 1, it is called a __________ ____________.
To write a rate as a unit rate, divide the numerator and denominator of the rate by the denominator.
Example: 2 characters per second

10. Heart Rate Activity
Use the “Every Beat of your Heart” worksheet to compare beats and time in order to find rates.

11. Examples
Express each rate as a unit rate. Round to the nearest tenth if necessary.
$11 for 4 boxes of cereal
400 miles on 14 gallons of gasoline

12. Compare Unit Rates You can also compare unit rates to solve problems.
Once you know the unit rate, you can use it to solve problems involving any amount.

13. Example
A store sells two different sizes of the same brand of sun screen, an 8-ounce bottle for $5.76 and a 12-ounce bottle for $8.88. Which size bottle is the better buy per ounce? Explain.

14. H.O.T. Problem
1. In which situation will the rate x miles/ y hours decrease? Give an example to explain your reasoning.
A. x increases, y is unchanged
B. x is unchanged, y increases

15. Essential Question
How are ratios and rates used in the real world? Provide examples to support your reasoning.
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