1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Write each fraction in simplest form. 1. 2.
Warm Up
Write each fraction in simplest form. 2 6 __ 1 3 __ 4 16 __ 1 4 __ 25 70
___ 5 14 __ 6 52 __ 3 26 __

3. What three consecutive odd numbers are factors of 105?
Problem of the Day
What three consecutive odd numbers are factors of 105?
3, 5, 7

4. Sunshine State Standards
MA.6.A.2.2 Interpret and compare ratios and rates.

5. Vocabulary
ratios
equivalent ratios
rate
unit rate

6. For a time, a local symphony orchestra was made up of 95 musicians.
Trombones
Harp
Percussion
Trumpets
Basses
Violas 3 6
Horns 1 4
Clarinets 5 8
Double reeds
Flutes 9 10
Cellos 12 29
Violins
You can compare the different groups by using ratios. A ratio is a comparison of two quantities using division.

7. For example, you can use a ratio to compare the number of violins (29) with the number of violas (12). This ratio can be written in three ways. 29 12
___
29 to 12
29:12
Terms 29 12
___
Notice that the ratio of violins to violas, is
different from the ratio of violas to violins, The order of the terms is important. 12 29
___
Ratios can be written to compare a part to a part, a part to the whole, or the whole to a part.

8. Read the ratio as “twenty-nine to twelve.”
Reading Math 29 12
___
Read the ratio as “twenty-nine to twelve.”

9. Additional Example 1A: Writing Ratios
Use the table to write the ratio.
cats to rabbits 2
Rabbits 7
Dogs 5
Cats
Animals at the Vet
or 5 to 2 or 5:2 5 2 __
Part to part

10. Additional Example 1B: Writing Ratios
Use the table to write the ratio.
dogs to total number of pets 2
Rabbits 7
Dogs 5
Cats
Animals at the Vet
or 7 to 14 or 7:14 7 14 __
Part to whole

11. Additional Example 1C: Writing Ratios
Use the table to write the ratio.
total number of pets to cats 2
Rabbits 7
Dogs 5
Cats
Animals at the Vet
or 14 to 5 or 14:5 14 5 __
Whole to part

12. Check It Out: Example 1A
Use the table to write each ratio. 3
Snakes 9
Hamsters 6
Birds
Animals at the Vet
birds to total number of pets
or 6 to 18 or 6:18 6 18 __ 1 _
Also
or 1 to 3 or 1 : 3 3

13. Check It Out: Example 1B
Use the table to write the ratio or rates.
snakes to hamsters 3
Snakes 9
Hamsters 6
Birds
Animals at the Vet
or 3 to 9 or 3:9 3 9 __ 1 _
or 1 to 3 or 1 : 3
Also 3

14. Equivalent ratios are ratios that name the same comparison
Equivalent ratios are ratios that name the same comparison. You can find an equivalent ratio by multiplying or dividing both terms of a ratio by the same number.

15. Additional Example 2: Writing Equivalent Ratios
Write three equivalent ratios to compare the number of diamonds to the number of spades in the pattern.
number of diamonds 3 6 __
There are 3 diamonds and 6 spades. =
number of spades 3 6 __
3 ÷ 3
6 ÷ 3
____ 1 2 __
There is 1 diamond for every 2 spades. = = 3 6 __
3 • 3
6 • 3 9 18 __
If you triple the pattern, there will be 9 diamonds for 18 spades. = =
So , , and are equivalent ratios. 3 6 __ 1 2 9 18

16. Check It Out: Example 2
Write three equivalent ratios to compare the number of triangles to the number of hearts in the pattern.
Possible answer : , and 3 9 __ 1 27

17. A rate compares two quantities that have different units of measure
A rate compares two quantities that have different units of measure. Suppose a 2-liter bottle of soda costs $1.98.
price
number of liters
_____________
$1.98
2 liters
________
rate = =
$1.98 for 2 liters
When the comparison is to one unit, the rate is called a unit rate. Divide both terms by the second term to find the unit rate.
$1.98 2
_____
$1.98 ÷ 2
2 ÷ 2
________
$0.99 1
_____
unit rate = = =
$0.99 for 1 liter
When the prices of two or more items are compared, the item with the lowest unit rate is the best deal.

18. Additional Example 3: Consumer Application
A 3-pack of paper towels costs $ A 6-pack of the same paper towels costs $5.46. Which is the better deal?
$2.79
3 rolls
_____
$5.46
6 rolls
_____
Write the rate.
Write the rate.
$2.79 ÷ 3
3 rolls ÷ 3
_________
Divide both terms by 3.
$5.46 ÷ 6
6 rolls ÷ 6
_________
Divide both terms by 6.
$0.93
1 roll
_____
$0.91
1 roll
_____
$0.93 for 1 roll.
$0.91 for 1 roll.
The 6-pack of paper towels is the better deal.

19. Check It Out: Example 3A
A 3-pack of juice boxes costs $2.10. A 9-pack costs $5.58. Which is the better deal?
$2.10 3
_____
$5.58 9
____
= $0.70 per box;
= $0.62 per box
The 9-pack is a better deal.

20. Check It Out: Example 3B
A 24 oz bottle of apple juice costs $5.76. A 12 oz bottle of apple juice costs $3.84. Which is the better deal?
$5.76 24
_____
$3.84 12
____
= $0.24 per oz;
= $0.32 per oz
The 24 ounce bottle is a better deal.

21. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

22. Use the table to write each ratio. 1. tulips to daffodils
Lesson Quiz
Use the table to write each ratio.
1. tulips to daffodils
2. crocuses to total number of bulbs
3. total bulbs to lilies
4. A dozen eggs cost $1.25 at one market. At a competing market, 1 dozen eggs cost $ Which is the better buy?
9:17
20:51
51:5 1 2 __
eggs from the first market

23. Lesson Quiz for Student Response Systems
1. Use the table to identify the ratio of lions to elephants.
A. 8:7
B. 8:12
C. 7:8
D. 7:12
Animals in a Zoo
Lions 8
Tigers 12
Elephants 7
Others 15

24. Lesson Quiz for Student Response Systems
2. Use the table to identify the ratio of game CDs to total number of CDs.
A. 25:8
B. 17:8
C. 8:17
D. 8:25
Gina’s CD Collection
Music 5
Games 8
Cartoons 12

25. Lesson Quiz for Student Response Systems
3. Use the table to identify the ratio of total number of grades to number of students with a C.
A. 9:30
B. 9:21
C. 21:9
D. 30:9
Grades on Final Exam A 8 B 13 C 9

26. Lesson Quiz for Student Response Systems
4. Jeff sells a pack of 36 pencils for $3.25. Betsy sells a pack of 12 pencils for $1.50. Which is the better buy?
A. a pack of 12 pencils from Betsy
B. a pack of 36 pencils from Jeff
C. Both
D. None