Download - 2.6 Write Ratios and Proportions
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2.6 Write Ratios and ProportionsEssential Question: How do you find ratios
and write and solve proportions?Warm-up:
CommonCoreCC.9-12.A.CED.1Create equations and in one variable and usethem to solveproblems.
Solve the equation1. 5/6x = 252. 2/3(6x + 3) = 143. g/5 – 7 = 124. You buy three identical polyester
film balloons and a birthday card. The card costs $3.95. Find the cost of each balloon if your total bill before tax was $33.80
9-17-13
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Ratios
• A ratio uses division to compare two quantities. You can write the ratio of two quantities a and b, where b is not equal to 0, in three ways.
• a to b a:b a/b• Each ratio is read “the ratio of a to
b.” Ratios should be written in simplest form.
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Write a ratio
EXAMPLE 1
VOLLEYBALL
A volleyball team plays 14 home matches and 10 away matches.
a. Find the ratio of home matches to away matches.
SOLUTION
= 75a.
home matches
away matches
14 10 =
b. Find the ratio of home matches to all matches.
b.home matches
all matches
14 14 + 10
= = 1424
= 712
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EXAMPLE 1
Derek and his brother decide to combine their CD collections. Derek has 44 CDs, and his brother has 52 CDs. Find the specified ratio.
1. The number of Derek’s CDs to the number of his brother’s CDs.
2. The number of Derek’s CDs to the number of CDs in the entire collection.
GUIDED PRACTICE for Example 1
1113
ANSWER
1124
ANSWER
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Proportions
• A proportion is an equation that states that two ratios are equivalent. The general form of a proportion is given below:
where b
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Solve a proportion
EXAMPLE 2
11 6
x30= Write original proportion.
Multiply each side by 30.
330 6
= x Simplify.
55 = x Divide.
11 6
x30=30 30
x30
Solve the proportion 11 6 = .
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EXAMPLE 2
Solve the proportion. Check your solution.
GUIDED PRACTICE for Example 2
4 7
w35 =3.
20ANSWER
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EXAMPLE 2
Solve the proportion. Check your solution.
GUIDED PRACTICE for Example 2
m12
92 =4.
54ANSWER
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EXAMPLE 2
Solve the proportion. Check your solution.
GUIDED PRACTICE for Example 2
5 9
z54 =5.
30ANSWER
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Solve a multi-step problem
EXAMPLE 3
ELEVATORS
The elevator that takes passengers from the lobby of the John Hancock Center in Chicago to the observation level travels 150 feet in 5 seconds. The observation level is located on the 94th floor, at 1029 feet above the ground. Find the time it takes the elevator to travel from the lobby to the observation level.
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Solve a multi-step problem
EXAMPLE 3
SOLUTION
STEP 2
Solve the proportion.
Write a proportion involving two ratios that compare the amount of time the elevator has ascended with the distance traveled.
STEP 1
x
1029=
5 Seconds
150 feet
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Solve a multi-step problem
EXAMPLE 3
5
150
x
1029= Write proportion.
5150
=1029 1029x
1029Multiply each side by 1029.
5145
150= x Simplify.
34.3 = x Use a calculator.
ANSWER
The elevator travels from the lobby to the observation level in 34.3 seconds.
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Solve a multi-step problem
EXAMPLE 3
You can use a table to check the reasonableness of your answer.
CHECK
The solution, 34.3 seconds, is slightly less than 35 seconds, and 1029 feet is slightly less than 1050 feet. So, the solution is reasonable.
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GUIDED PRACTICE for Example 3
WHAT IF? In Example 3, suppose the elevator travels 125 feet in 5 seconds. Find the time it will take for elevator to travel from the lobby to the observation level.
6.
ANSWER
41.16 sec
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GUIDED PRACTICE for Example 3
When two full moons appear in the same month. The second full moon is called a blue moon. On average, 2 blue moons occur every 5 years. Find the number of blue moons that are likely to occur in the next 25 years.
7.
ASTRONOMY
ANSWER
10 blue moons
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Classwork/Homework
2.6 Exercises 2-54 even pages 117 to 119