1. Ratios, Rates, Unit Rates

2. Warm-up
Simplify the fraction 1) 3/12 2) 6/18 3) 12/96 4) 4/16 5) 8/72

3. Objectives As a learner I will… Express ratios in all three forms
Simplify ratios
Write rates
Find unit rates

4. Vocabulary
Ratio – a comparison of two quantities by division Equivalent ratios – ratios that names the same comparison Rate – a ratio that compares two quantities measured in different units Unit Rate – a rate in which the second quantity in the comparison is one unit

5. Brain Pop

6. Key Concept: Expressing Ratios
There are three ways to express a ratio:
Words
Fraction
Colon

7. Key Concept: Reading a Ratio
Animals at the Vet
Cats 5
Dogs 7
Rabbits 2
Horses 3
The ratio of cats to dogs is: 5 7
To read a ratio, we use the word “to”
You read this ratio as:
“5 to 7”

8. Key Concept: Simplifying Ratios
Ratios are like fractions, therefore, we have to simplify them in the same way For example: The ratio of boys to girls in a particular class is 7 to 14, 7/14 or 7:14 7 would simplify to be 1 1:2 1 to

9. Example 1 Animals at the Vet Cats 15 Dogs 5 Rabbits 2 Horses 3
Write each ratio in simplest form.
Write the ratio of cats to rabbits
Write a ratio of dogs to horses
Write the ratio of horses to rabbits
Write the ratio of rabbits to horses

10. Key Concept: Equivalent Ratios
Ratios that name the same comparison Example 2: Write three equivalent ratios to compare the number of diamonds to the number of clubs. ♦♦♦♦ ♣♣♣♣♣♣

11. Key Concept: Rates
From our definition, we know a rate is a type of ratio. It compares different units of measure.
For example:
Miles per hour
Cost per unit

12. Key Concept: Rates
Example 3: A 2-liter of soda costs $1.98. Write this as a rate.
Rate = price = $1.98
# of liters 2 liters
Example 4: A car drives 99 miles in 3 hours
Rate = distance = 99 miles
time hours

13. Key Concept: Unit Rates
Unit Rates are a type of rate. Unit rates is a comparison to one unit.
To find a unit rate, divide by the number in the denominator.

14. Key Concept: Unit Rates
Using the same examples:
Example 5: A 2-liter of soda costs $ Write this as a rate.
Unit Rate = price = $ ÷ 2 = $0.99
# of liters 2 liters ÷ liter
Example 6: A car drives 99 miles in 3 hours
Unit Rate = distance = 99 miles = 33 miles
time hours hour

15. Independent Practice
There are 14 white marbles and 8 red marbles. Write a simplified ratio of white to red marbles in all three forms.
Write a rate to express the following: Sarah paid $35.00 for 5 pairs of jeans
Write a unit rate to express the following: Janet ran 68 yards in 2 minutes.

16. Unit Rates Grocery Ad Activity