1. Lesson 6.1 Ratios and Rates
Essential Question: How do you find ratios and unit rates?

2. Before we start… There are 14 girls in a class of 24 students.
What fraction of the class is girls?
What fraction of the class is boys?
What is the fraction of girls to boys in class?

3. 𝑎 𝑏 𝑎:𝑏 a to b What is a ratio? Uses division to compare two numbers.
You can write the ratio of a to b as:
𝑎 𝑏 𝑎:𝑏 a to b

4. What are equivalent ratios?
Ratios that have the same value.
9:5, 18:10, 3:1 2 3

5. How do you write a ratio?
To write a ratio, you make a fraction comparing the two numbers.
Put the ratio in simplest form by reducing.

6. Archery An archer shoots 60 arrows at a target, with 44 arrows hitting the scoring area and 16 missing the scoring area.
Write the ratio of hits to the number of misses
Write the ratio of hits to the number of shots

7. Volleyball A volleyball team plays 14 home matches and 10 away matches.
a. Find the ratio of home matches to away matches.
b. Find the ratio of home matches to all matches.

8. Skiing A ski resort has 15 easy, 25 intermediate, 7 difficult, and 11 expert-only trails. Write the ratio “intermediate trails: easy trails” in three ways.

9. Average wing length (cm)
Biology The ratio comparing the length of a bird’s wings to the average width of the bird’s wings is the bird’s aspect ratio. Order the birds in the table from the greatest aspect ratio to the least.
Bird
Wing length (cm)
Average wing length (cm)
White-tailed eagle
209 30
European jay 47 12
Black-headed gull 83 8

10. What is a rate? A ratio of two quantities that have different units.
Equivalent = same value

11. Weather Lightning strikes about 100 times per second around the world
Weather Lightning strikes about 100 times per second around the world. About how many times does lightning strike per minute around the world?

12. Typing Li types 75 words per minute
Typing Li types 75 words per minute. How many words can she type in an hour at this rate?

13. Pumping Water A water pump moves 2 gallons of water per second
Pumping Water A water pump moves 2 gallons of water per second. How many gallons of water are pumped per minute?

14. What is a unit rate? 55 miles per hour
A rate that has a denominator of 1 unit.
55 miles per hour
$2.99 per pound

15. How do you find a unit rate?
To find a unit rate, divide the numerator and the denominator by the denominator.
You want a denominator of 1

16. Write -24 feet per 5 seconds as a unit rate.

17. Write the rate as a unit rate. 114 points 6 games

18. Write the rate as a unit rate. 365 people 5 months

19. Write the rate as a unit rate. 329 miles 10 gallons

20. Party You host a party for 12 people
Party You host a party for 12 people. The food and drinks for the party cost $66. What is the cost per person?

21. How do you find ratios and unit rates?

22. Ticket Out the Door
You pay $3.45 for 15 ounces of cereal. What is the cost per ounce?