Course 3 5-4 Solving Proportions 5-4 Solving Proportions Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.

Course 3

5-4 Solving Proportions5-4 Solving Proportions

Course 3

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 3

5-4 Solving Proportions

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

35

1.

4530

3. 9060

32

,

1012

2. 2024

56

,

89

4. 2427

1618

,

915

610

,Possible answers:

Course 3


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:

Course 3


Learn to solve proportions.

Course 3


Vocabulary

cross product

Course 3


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 proportion is true:

mass 2length 1

mass 1length 2

=

Mass 1

Mass 2

Fulcrum

Length 1 Length 2

Course 3


One way to find whether ratios, such as those on

the previous slide, are equal is to find a common

denominator. Since and ,

.

7296

68

= 7296

912

=

912

68

=

Course 3


Course 3


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

Helpful Hint

Course 3


Tell whether the ratios are proportional.

410

615

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

Course 3


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 equal ratios.

Find the cross products.

Additional Example 1B: Using Cross Products to Identify Proportions

Course 3


Tell whether the ratios are proportional.

Check It Out: Example 1A

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

20

20 = 20

Find cross products.2024

510

24

510

=?

Course 3


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?

Check It Out: 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 equal ratios.


Course 3


Solve the proportion .

x ÷ 15 = 16

Find the unit rates.

The numerators are equal because the denominators are equal.

Additional Example 2: Solving Proportions Using Unit Rates

$483 items

$x15 items

=

$161 item

$(x ÷ 15)1 item

=

Multiply both sides by 15.15(x ÷ 15) = 16(15)

x = 240 Simplify.

Course 3



x ÷ 18 = 15

Find the unit rates.


Check It Out: Example 2

$604 items

$x18 items

=

$151 items

$(x ÷ 18)1 item

=

Multiply both sides by 18.18(x ÷ 18) = 15(18)

x = 270 Simplify.

Course 3



1y = 7

Multiply to write the fractions with the LCD.


13

y21

=

Divide both sides by 1.71

1y1

=

Additional Example 3: Using Equivalent Fractions

=(y • 1)(21 • 1)

(1 • 7)(3 • 7)

1y21

= 721

y = 7 Simplify.

Course 3



1y = 12

Multiply to write the fractions with the LCD.


34

y16

=

Divide both sides by 1.121

1y1

=


=(y • 1)(16 • 1)

(3 • 4)(4 • 4)

1y16

=1216

y = 12 Simplify.

Course 3


J & A Department Store is selling 3 pairs of children’s socks for $5. Mrs. Wagner wants to buy a dozen pairs of socks. How much will this cost?

12 pairs3 pairs = 4

4 x $5 = $20

Set up the proportion.

Divide to find the factor of change.

A dozen pairs of socks will cost $20.

Additional Example 4: Business Application

3 pairs$5.00

= 12 pairs$d

1 dozen pairs of socks = 12 pairs of socks

Multiply by the factor of change to find cost.

Course 3


The Hardware Store is selling 6 light bulbs for $7. Mr. Raynold wants to buy 3 dozen light bulbs. How much will this cost?

36 bulbs6 bulbs

= 6

6 x $7 = $42


Divide to find the factor of change.

3 dozen light bulbs will cost $42.


6 bulbs$7.00

= 36 bulbs$d

3 dozen light bulbs = 36 light bulbs

Multiply by the factor of change to find cost.

Course 3


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


Let x represent Marco’s weight.


Multiply.

Solve. Divide both sides by 5.

Marco weighs 44 lb.

Additional Example 5: Physical Science Application

220 = 5x

55 • 4 = 5x

x4

555

=

mass 1length 2

= mass 2length 1

Course 3


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?


6x6

4506

=

75 = x


Let x represent Sharon’s weight.


Multiply.

Solve. Divide both sides by 6.

Sharon weighs 75 lb.

450 = 6x

90 • 5 = 6x

x5

906

=

mass 1length 2

= mass 2length 1

Course 3


Lesson Quiz

Tell whether each pair of ratios is proportional.

4842 =? 16

141. 40

15 =? 34

2.

Solve each proportion.

3. 4.

5. Two weights are balanced on a fulcrum. If a 6 lb 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 =

Course 3 5-4 Solving Proportions 5-4 Solving Proportions Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.

Documents

equal ratios

equal distance

cross products

additional example

example 1b3

following proportion

dozen light bulbs

pairs of socksmultiply