2.7 Solving Proportions Using Cross ProductsEssential Question: How do you solve proportions using

cross products?

Warm-up: Solve the proportion.CommonCoreCC.9-12.A.CED.1CC.9-12.A.REI.3

1.

2.

3.

4.

5-19-15

3(2x – 1) – 11 = -2(1- x )

7x – 29 – 21x = 3 – (12 + 2x)

63820155

2 ppp

11

7

11

32

11

13 xx

2.6 Exercises 2-54 even• 2) ½ , 1:2, 1 to 2• 4) yes 6) no, 7 to 8• 8) 64 10) 6 12) 5• 14) 4 16) 48 18) 56• 20) B 22) Multiply

each side by 10, not one side by 10 and the other side by 20

25,20

5010

1010 m

m

24) 35 26) 36 28) 130) 30 32) 3.3 34) 236) 6 38) 4 40) 1942) 4 44) yes 46) 7/8 48) 3/5 50) 21 pages52) a) 70.3 ft b)

Width (ft)

Length (ft)

20 37

25 46.25

30 55.5

35 64.75

40 74

54)

142

5113

10

x

x

a)

b)

c. Your friend

Cross Products Property

• Words The cross products of a proportion are equal.

• Example

• Algebra 2483

2464

bcadthendandbwhered

c

b

aIf ,0 0

Use the cross products property

EXAMPLE 1

Write original proportion.

8 15 = x 6

Solve the proportion = .8 x

615

Cross products property

Simplify.120 = 6x

Divide each side by 6.20 = x

The solution is 20. Check by substituting 20 for x in the original proportion.

ANSWER

=8 x

615

Use the cross products property

EXAMPLE 1

Substitute 20 for x.

CHECK

Cross products property

Simplify. Solution checks.

820

615

=?

8 15 = 20 6?

120 = 120

EXAMPLE 2 Standardized Test Practice

What is the value of x in the proportion = ?4x

83x –

A – 6 B – 3 C3

D 6

SOLUTION

4x = 8

x – 3 Write original proportion.

Cross products property4(x – 3) = x 8

4x – 12 = 8x Simplify.

Subtract 4x from each side. –12 = 4x

Divide each side by 4. –3 = x

EXAMPLE 2 Standardized Test Practice

The value of x is –3. The correct answer is B.

ANSWER

A B C D

Write and solve a proportion

EXAMPLE 3

x280=

8 amount of food100 weight of seal

SOLUTION

STEP 1Write a proportion involving two ratios that compare the amount of food with the weight of the seal.

Each day, the seals at an aquarium are each fed 8 pounds of food for every 100 pounds of their body weight. A seal at the aquarium weighs 280 pounds.How much food should the seal be fed per day?

Seals

Write and solve a proportion

EXAMPLE 3

STEP 2Solve the proportion.

8100

x280= Write proportion.

8 280 = 100 x Cross products property

2240 = 100x Simplify.

22.4 = x Divide each side by 100.

ANSWER

A 280 pound seal should be fed 22.4 pounds of food perday.

EXAMPLE 1

Solve the proportion. Check your solution.

GUIDED PRACTICE for Examples 1, 2, and 3

=4 a

2430

1.

5ANSWER

EXAMPLE 2GUIDED PRACTICE for Examples 1, 2, and 3

3x = 2

x – 6 2.

18ANSWER

Solve the proportion. Check your solution.

EXAMPLE 2GUIDED PRACTICE for Examples 1, 2, and 3

4m5 = m – 6 3.

18ANSWER

Solve the proportion. Check your solution.

EXAMPLE 3GUIDED PRACTICE for Examples 1, 2, and 3

20.8ANSWER

Solve the proportion. Check your solution.

WHAT IF? In Example 3, suppose the seal weighs 260 pounds. How much food should the seal be fed per day?

4.

EXAMPLE 4 Use the scale on a map

Maps

Use a metric ruler and the map of Ohio to estimate the distance between Cleveland and Cincinnati.

SOLUTION

From the map’s scale, 1 centimeter represents 85 kilometers. On the map, the distance between Cleveland and Cincinnati is about 4.2 centimeters.

EXAMPLE 4 Use the scale on a map

Write and solve a proportion to find the distance d between the cities.

=4.2 d

1 centimeters85 kilometers

Cross products property

d = 357 Simplify.

ANSWER

The actual distance between Cleveland and Cincinnati is about 357 kilometers.

1 d = 85 4.2

EXAMPLE 4 Use the scale on a mapGUIDED PRACTICE for Example 4

5.

Use a metric ruler and the map in Example 4 to estimate the distance (in kilometers) between Columbus and Cleveland.

about 212.5 kmANSWER

EXAMPLE 4 Use the scale on a mapGUIDED PRACTICE for Example 4

6.

The ship model kits sold at a hobby store have a scale of 1 ft : 600 ft. A completed model of the Queen Elizabeth II is 1.6 feet long. Estimate the actual length of the Queen Elizabeth II.

Model ships

ANSWER about 960 ft

Classwork/homework

•3.6 Practice B