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EXAMPLE 1. Writing a Ratio in Different Ways. Music. In some school orchestras, all of the instruments are stringed: violins,violas, cellos, and double basses. How can you compare the numbers of instruments in the orchestra?. 8. 35. Violas. Total instruments. EXAMPLE 1.

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Writing a Ratio in Different Ways

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Writing a ratio in different ways

EXAMPLE 1

Writing a Ratio in Different Ways

Music

In some school orchestras, all of the instruments are stringed: violins,violas, cellos, and double basses. How can you compare the numbers of instruments in the orchestra?


Writing a ratio in different ways

8

35

Violas

Total instruments

EXAMPLE 1

Writing a Ratio in Different Ways

In the orchestra shown above, 8 of the 35 instruments are violas. The ratio of the number of violas to the total

number of instruments, , can be written

as ,as 8 : 35, or as 8 to 35.


Writing a ratio in different ways

1

1 3

Double basses

3

1

=

=

=

Cellos

6

2 3

2

1

The ratio is , or 1 to 2, so there is 1 double bass for every 2 cellos.

ANSWER

1

2

EXAMPLE 2

Writing Ratios in Simplest Form

Use the diagram below. Write the ratio of the number of double basses to the number of cellos in simplest form.


Writing a ratio in different ways

ANSWER

ANSWER

18

8

, 18 : 35,

18to 35

35

3

, 8 : 3, 8 to 3

for Examples 1 and 2

GUIDED PRACTICE

In Exercises 1 and 2, write the ratio in three ways.

1.violins to total instruments

2.violas to double basses


Writing a ratio in different ways

ANSWER

1

, 1 : 3, 1to3

3

for Examples 1 and 2

GUIDED PRACTICE

3.Write the ratio of cellos to violins in simplest form.


Writing a ratio in different ways

SOLUTION

Think about the denominators of the two fractions.

5 4

5

20

=

60

15

15 4

ANSWER

5

20

=

15

60

EXAMPLE 3

Writing an Equivalent Ratio

5

?

Complete the statement to write equivalent ratios.

=

15

60


Writing a ratio in different ways

SOLUTION

Write each ratio as a decimal. Then compare the decimals.

7

3

Sofia:

Mike:

7out of10

0.7

=

0.75

=

=

10

4

ANSWER

Because 0.75>0.7, Sofia has the better record.

EXAMPLE 4

Comparing Ratios Using Decimals

3

Football Sofia completes of her passes. Mike

completes 7 out of every 10 passes. Who has the better

record?

4


Writing a ratio in different ways

2

20

5

?

6.

4.

=

=

7

35

32

3

?

15

5.

=

?

50

10

20

5

2

35

7

=

=

ANSWER

ANSWER

=

ANSWER

8

3

32

15

10

50

for Examples 3 and 4

GUIDED PRACTICE

Copy and complete the statement.


Writing a ratio in different ways

5

3

4

?

18out of30

2 : 4 ? 7 : 35

7.

8.

9.

?

20

5

10

3

5

2

4

7

=

18out of30

>

<

5

20

4

10

35

for Examples 3 and 4

GUIDED PRACTICE

Copy and complete the statement using <, >, or =.


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