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RATIOS AND RATES

You can compare the different groups by using ratios. A ratio is a comparison of two quantities using division.

For a time, a local symphony orchestra was made up of 95 musicians.

Trombones

Harp

Percussion

Trumpets

Basses

Violas

36Horns

14Clarinets

58Double reeds

35Flutes

910Cellos

1229Violins

VOCABULARY

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.

Notice that the ratio of violins to violas, is

different from the ratio of violas to violins, . The order of the terms is important.

29 12___

29 12___

12 29___

29 to 12 29:12Terms

Ratios can be written to compare a part to a part, a part to the whole, or the whole to a part.

Read the ratio as “twenty-nine to twelve.”

Reading Math29

12___

Example 1: Writing Ratios

Use the table to write the ratio.

cats to rabbits

2Rabbits

7Dogs

5Cats

Animals at the Vet

Example 2: Writing Ratios

Use the table to write the ratio.

total number of pets to cats

2Rabbits

7Dogs

5Cats

Animals at the Vet

3Snakes

9Hamsters

6Birds

Animals at the Vet

Use the table to write each ratio.

Example 3

birds to total number of pets

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.

VOCABULARY

Example 4: Writing Equivalent Ratios

Write three equivalent ratios to compare the number of diamonds to the number of spades in the pattern.

Example 5

Write three equivalent ratios to compare the number of triangles to the number of hearts in the pattern.

A rate compares two quantities that have different units of measure. Suppose a 2-liter bottle of soda costs $1.98.

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.

When the prices of two or more items are compared, the item with the lowest unit rate is the best deal.

rate =price

number of liters_____________ $1.98

2 liters ________= $1.98 for 2 liters

unit rate =$1.98

2 _____ $1.98 ÷ 2

2 ÷ 2 ________= $0.99 for 1 liter=

$0.99 1 _____

VOCABULARY

Example 6: Real-World Application

A 3-pack of paper towels costs $2.79. A 6-pack of the same paper towels costs $5.46. Which is the better deal?

Example 7

A 3-pack of juice boxes costs $2.10. A 9-pack costs $5.58. Which is the better deal?

Example 8

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?