Transcript la1_ch02_06 write ratios and proportions_teacher

2.6 Write Ratios and Proportions
• You will find ratios and
write and solve
proportions.
• Essential Question:
How do you find ratios
and write and solve
proportions?
EXAMPLE
Warm-Up1Exercises
Write a ratio
VOLLEYBALL
A volleyball team plays 14 home matches and 10 away
matches.
a.
Find the ratio of home matches to away matches.
b.
Find the ratio of home matches to all matches.
SOLUTION
home matches
7
14
a.
= 10 = 5
away matches
b.
home matches
all matches
=
14
14
7
14 + 10 = 24 = 12
EXAMPLE
1Exercises
Warm-Up
GUIDED
PRACTICE
for 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.
ANSWER
11
13
2. The number of Derek’s CDs to the number of CDs in
the entire collection.
ANSWER
11
24
EXAMPLE
Warm-Up2Exercises
Solve a proportion
Solve the proportion 11 = x .
30
6
30
11 x
6 = 30
Write original proportion.
x
11
6 = 30 30
Multiply each side by 30.
330 x
=
6
55 = x
Simplify.
Divide.
EXAMPLE
2Exercises
Warm-Up
GUIDED
PRACTICE
for Example 2
Solve the proportion. Check your solution.
3.
4
w
=
7
35
ANSWER 20
EXAMPLE
2Exercises
Warm-Up
GUIDED
PRACTICE
for Example 2
Solve the proportion. Check your solution.
m
9
4. 2 = 12
ANSWER
54
EXAMPLE
2Exercises
Warm-Up
GUIDED
PRACTICE
for Example 2
Solve the proportion. Check your solution.
5
z
5. 54 = 9
ANSWER
30
EXAMPLE
Warm-Up3Exercises
Solve a multi-step problem
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.
EXAMPLE
Warm-Up3Exercises
Solve a multi-step problem
SOLUTION
STEP 1
Write a proportion involving two ratios that compare
the amount of time the elevator has ascended with the
distance traveled.
5
150
x
=
1029
STEP 2
Solve the proportion.
Seconds
feet
EXAMPLE
Warm-Up3Exercises
Solve a multi-step problem
5
x
=
150 1029
x
5
1029
= 1029
1029
150
5145
150
= x
34.3 = x
Write proportion.
Multiply each side by 1029.
Simplify.
Use a calculator.
ANSWER
The elevator travels from the lobby to the observation
level in 34.3 seconds.
EXAMPLE
Warm-Up3Exercises
Solve a multi-step problem
CHECK
You can use a table to check the reasonableness of
your answer.
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.
Warm-Up
Exercises
GUIDED
PRACTICE
6.
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.
ANSWER
41.16 sec
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 3
ASTRONOMY
7. 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.
ANSWER
10 blue moons
Daily
Homework
Quiz
Warm-Up
Exercises
1.
1
A chocolate chip cookie recipe calls for 2
4
3
cups of flour and
cup of brown sugar. Find
4
the ratio of brown sugar to flour.
ANSWER
1
3
Solve the proportion.
2.
a
9
=
7 21
ANSWER
3
Daily
Homework
Quiz
Warm-Up
Exercises
Solve the proportion.
3.
m
32
=
28 14
ANSWER
4.
16
A printer can print 12 color pages in 3 minutes.
How many color pages can the printer print in
9 minutes? Write and solve a proportion to find
the answer.
ANSWER
12
x
3 = 9 ; 36 color pages
• You will find ratios and
write and solve
proportions.
• Essential Question:
How do you find ratios
and write and solve
proportions?
• Ratios compare two quantities.
• A proportion states that two
ratios are equivalent. When
writing a proportion, put like
quantities
in the same location in each
ratio, such as nuts = nuts
ounces ounces
A ratio is an expression that
relates one quantity to another by
division, while a proportion is an
equation of two ratios. Solve
proportions
with unknown numbers in
the same way as you solve
equations,
by isolating the variable.