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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
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