1. Learn to write ratios and rates and to find unit rates.

2. Vocabulary
ratios
equivalent ratios
rate
unit rate

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

4. 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.

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

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

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

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

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

10. Check It Out: Example 1B
Use the table to write the ratio.
snakes to birds
Animals at the Vet
Birds 6
Hamsters 9
Snakes 3
or 3 to 6 or 3:6 3 6 __
Part to part

11. Check It Out: Example 1C
Use the table to write the ratio.
total number of pets to hamsters
Animals at the Vet
Birds 6
Hamsters 9
Snakes 3
or 18 to 9 or 18:9 18 9 __
Whole to part

12. 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.

13. 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

14. There are 3 triangles and 9 hearts. number of hearts
Check It Out: Example 2
Write three equivalent ratios to compare the number of triangles to the number of hearts in the pattern.
number of triangles 3 9 __
There are 3 triangles and 9 hearts. =
number of hearts 3 9 __
3 ÷ 3
9 ÷ 3
____ 1 3 __
There is 1 triangle for every 3 hearts. = =
If you triple the pattern, there will be 9 triangles for 27 hearts. 3 9 __
3 • 3
9 • 3 9 27 __ = =
So , , and are equivalent ratios. 3 9 __ 1 27

15. 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.

16. 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.

17. Check It Out: Example 3
A 3-pack of juice boxes costs $2.10. A 9-pack of the same juice boxes costs $5.58. Which is the better deal?
$2.10
3 pack
_____
$5.58
9 pack
_____
Write the rate.
Write the rate.
$2.10 ÷ 3
3 pack ÷ 3
_________
Divide both terms by 3.
$5.58 ÷ 9
9 pack ÷ 9
_________
Divide both terms by 9.
$0.70
1 box
_____
$0.62
1 box
_____
$0.62 for 1 juice box.
$0.70 for 1 juice box.
The 9-pack of juice boxes is the better deal.

18. 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 $2.00. Which is the better buy?
9:17
20:51
51:5 1 2 __
eggs from the first market