Lesson 7.1, For use with pages 343-346

Write the fraction in simplest form.

1. 1421

2. 2555

Lesson 7.1, For use with pages 343-346

Write the fraction in simplest form.

1. 1421

2. 2555

ANSWER 23

ANSWER 511

7.1 Ratios and Rates7.1 Ratios and Rates

Essential QuestionsEssential Questions

What is the connection What is the connection between a ratio and a between a ratio and a fraction?fraction?

Why are ratios and Why are ratios and proportions important?proportions important?

How are scale drawings, How are scale drawings, models, and proportions used models, and proportions used in everyday life?in everyday life?

Section 7.1Vocabulary:

Ratio – a comparison of two quantities(like quantities)

3 ways to write a ratio (all read the same)

3 to 4 3 : 4 3

4

RatiosRatios Ratios are similar to fractions because they

1) can be written like a fraction 2) can be simplified like a fraction 3) compare two things

Example: boys to girls in the classroom 12: 14 but can be simplified to

6: 7 ( for every 6 boys, there are 7 girls)

Vocabulary: RATE: a special kind of ratio in which

quantities using different units are compared.

Example: 15 oranges for $2.00 65 miles in one hour

$300 for 10 books

Vocabulary: Unit Rate: a comparison to 1 unit

(using the words like per mile, per minute, per inch – meaning in ONE)

Examples: 25 miles/gallon $43 / book

82 cents / picture(meaning: for ONE of these items)

Name some other “unit rates”.

Find the unit rate of each:

$80 for 4 hour

500 words in 10 minutes

175 students for 5 teachers

Tide detergent cost $5.98 for 46 oz., while a 75 oz. box costs $8.99. Which is the better buy?

When might a “larger” amount of some item not be the better buy?

A proportion is an equation stating that two ratios are equal.

For example:

If cross products are equal, the ratios form a proportion.

3 6

8 16

EXAMPLE 2 Using the Cross Products Property

6.815.4

= 40.8m Write original proportion.

Cross products property

Multiply.

6.8m6.8 =

628.326.8

Divide each side by 6.8.

m = 92.4 Simplify.

Check: You can check your solution by finding the cross products of the proportion. If the cross products are equal, the solution is correct.

6.8m = 15.4 (40.8)

6.8m = 628.32

EXAMPLE 2

Substitute 92.4 for m.

Multiply.6.8 (92.4) 15.4 (40.8)=?

628.32 628.32 =

?6.815.4

= 40.892.4

Using the Cross Products Property

GUIDED PRACTICE for Example 2

Solve the proportion. Then check your solution.

5. 6c = 54

99

Write original proportion.

6 (99) = 54c

594 = 54c

59454

54c 54=

=11 c

Cross products property

Multiply.

Divide each side by 54.

Simplify.

6c = 54

99

Check:

Substitute 11 for m.

Multiply.6 (99) 11 (54)=?

594 594=

? 6 11

= 5499

GUIDED PRACTICE for Example 2

GUIDED PRACTICE for Example 2

Solve the proportion. Then check your solution.

6. n14 = 63

84

84n = 14(63)

84n = 882

84n84

88284=

=n 10.5

Cross products property

Multiply.

Divide each side by 84.

Simplify.

Write original proportion.n14 = 63

84

GUIDED PRACTICE for Example 2

Check:

Substitute 10.5 for m.

Multiply.10.5 (84) 14 (63)=?

?10.5 14

= 6384

882 882=

GUIDED PRACTICE for Example 2

Solve the proportion. Then check your solution.

7. 2.10.9 = 27.3

y

2.1 y = 0.9(27.3)

2.1 y

= 24.57

2.1y2.1

24.572.1=

=y 11.7

Cross products property

Multiply.

Divide each side by 2.1.

Simplify.

Write original proportion.2.10.9 = 27.3

y

Check:

Substitute 11.7 for m.

Multiply.(2.1) (11.7) 0.9 (27.3)=?

24.5724.57=

GUIDED PRACTICE for Example 2

?2.1 0.9

= 27.311.7

HomeworkHomework

Page 345 #19-26 Page 351 #12-19