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 =

Documents

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