Ch. 7 Learning Goal: Ratios & Proportions• Learn to find equivalent ratios to create proportions (7-1)

• Learn to work with rates and ratios (7-2)

• Learn to use one or more conversion factors to solve rate problems (7-3)

• Learn to solve proportions (7-4)

• Learn to identify and create dilations of plane figures (7-5)

• Learn to determine whether figures are similar, to use scale factors, and to find missing dimensions similar figures (7-6)

• Learn to make comparisons between and find dimensions of scale drawings and actual objects (7-7)

• Learn to make comparisons between and find dimensions of scale models and actual objects (7-8)

• Learn to make scale models of solid figures (7-9)

Page 353 #8-14 Answers

Pre-Algebra

7-4 Solving Proportions

Pre-Algebra Homework

Page 358

#15-28Mid-Chapter 7 Chop Chop Quiz Tomorrow!

Pre-Algebra

7-4 Solving Proportions7-4 Solving Proportions

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

7-4 Solving Proportions

Warm UpFind two ratios that are equivalent to each given ratio.

Pre-Algebra

7-4 Solving Proportions

35

1.

4530

3. 9060

32

,

1012

2. 2024

56

,

89

4. 2427

1618

,

915

610

,Possible answers:

Pre-Algebra

7-4 Solving Proportions

Problem of the Day

Replace each • with a digit from 1 to 7 to write a proportion. Use each digit once. The digits 2 and 3 are already shown.

••

•23

••= 14

723

56=Possible answer:

Pre-Algebra

7-4 Solving Proportions

Today’s Learning Goal Assignment

Learn to solve proportions.

Pre-Algebra

7-4 Solving Proportions

Vocabulary

cross product

Pre-Algebra

7-4 Solving Proportions

Unequal masses will not balance on a fulcrum if they are an equal distance from it; one side will go up and the other side will go down.

Unequal masses will balance when the following proportions is true:

mass 2length 1

mass 1length 2

=

Mass 1

Mass 2

Fulcrum

Length 1 Length 2

Pre-Algebra

7-4 Solving Proportions

One way to find whether ratios, such as those above, are equal is to find a common denominator. The ratios are equal if their numerators are equal after the fractions have been rewritten with a common denominator.

7296

68

= 7296

912

=

912

68

=

Pre-Algebra

7-4 Solving Proportions

Pre-Algebra

7-4 Solving Proportions

The cross product represents the numerator of the fraction when a common denominator is found by multiplying the denominators.

Helpful Hint

Pre-Algebra

7-4 Solving Proportions

Tell whether the ratios are proportional.

410

615

A.

Since the cross products are equal, the ratios are proportional.

60

=?

Additional Example 1A: Using Cross Products to Identify Proportions

60 = 60

Find cross products.60410

615

Pre-Algebra

7-4 Solving Proportions

A mixture of fuel for a certain small engine should be 4 parts gasoline to 1 part oil. If you combine 5 quarts of oil with 15 quarts of gasoline, will the mixture be correct?

4 parts gasoline1 part oil

=? 15 quarts gasoline5 quarts oil

4 • 5 = 20 1 • 15 = 15

20 ≠ 15

The ratios are not equal. The mixture will not be correct.

Set up ratios.

Find the cross products.

Additional Example 1B: Using Cross Products to Identify Proportions

Pre-Algebra

7-4 Solving Proportions

Tell whether the ratios are proportional.

Try This: Example 1A

Since the cross products are equal, the ratios are proportional.

20

20 = 20

Find cross products.2024

510

24

510

A. =?

Pre-Algebra

7-4 Solving Proportions

A mixture for a certain brand of tea should be 3 parts tea to 1 part sugar. If you combine 4 tablespoons of sugar with 12 tablespoons of tea, will the mixture be correct?

Try This: Example 1B

3 parts tea 1 part sugar

=? 12 tablespoons tea4 tablespoons sugar

3 • 4 = 12 1 • 12 = 12

12 = 12

The ratios are equal. The mixture will be correct.

Set up ratios.

Find the cross products.

Pre-Algebra

7-4 Solving Proportions

When you do not know one of the four numbers in a proportion, set the cross products equal to each other and solve.

Pre-Algebra

7-4 Solving Proportions

Solve the proportion.

6p = 12 • 5

p = 10

6p = 60

Find the cross products.

Solve.

Additional Example 2: Solving Proportions

56

p12

=

; the proportion checks.56

1012

=

Pre-Algebra

7-4 Solving Proportions

Solve the proportion.

14 • 3 = 2g

21 = g

42 = 2g

Find the cross products.

Solve.

Try This: Example 2

23

14g

=

; the proportion checks.23

1421

=

Pre-Algebra

7-4 Solving Proportions

Allyson weighs 55 lbs and sits on a seesaw 4 ft away from its center. If Marco sits 5 ft away from the center and the seesaw is balanced, how much does Marco weigh?

5x5

2205

=

44 = x

Set up the proportion.

Let x represent Marco’s weight.

Find the cross products.

Multiply.

Solve. Divide both sides by 5.

Marco weighs 44 lb.

Additional Example 3: Physical Science Application

220 = 5x

55 • 4 = 5x

x4

555

=

mass 1length 2

= mass 2length 1

Pre-Algebra

7-4 Solving Proportions

Robert weighs 90 lbs and sits on a seesaw 5 ft away from its center. If Sharon sits 6 ft away from the center and the seesaw is balanced, how much does Sharon weigh?

Try This: Example 3

6x6

4506

=

75 = x

Set up the proportion.

Let x represent Sharon’s weight.

Find the cross products.

Multiply.

Solve. Divide both sides by 5.

Sharon weighs 75 lb.

450 = 6x

90 • 5 = 6x

x5

906

=

mass 1length 2

= mass 2length 1

Pre-Algebra

7-4 Solving Proportions

Lesson Quiz

Tell whether each pair of ratios is proportional.

4842 =? 16

141. 20

15 =? 34

2.

Solve each proportion.

3. 4.

5. Two weights are balanced on a fulcrum. If a 6lb weight is positioned 1.5 ft from the fulcrum, at what distance from the fulcrum must an 18 lb weight be placed to keep the weights balanced?

yes no

n = 30 n = 16

0.5 ft

4518

n12 = n

2469 =