• Solve Problems Using Ratios A Picture Is Worth . . .

Solve Problems Using Ratios
Activity 18
A Picture Is Worth . . .
Lesson 18-1 Solve Problems Using Ratios
Learning Targets:
Use ratio and rate reasoning to solve problems.
Use ratio reasoning to convert measurement units.
Apply quantitative reasoning, including predicting and comparing, to
solve real-world problems involving ratios and rates.
My Notes
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•
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SUGGESTED LEARNING STRATEGIES: Close Reading, Construct
Arguments, Create Representations, Identify a Subtask
Everyone tells Chris that his stories and drawings are great. Career Week
is coming at his school and Chris is very excited to meet someone who
has worked with movies and video game design. Chris decided to do
some research before Career Week and was surprised to find out how
much math is involved in filming and animation. Animation is a series of pictures that flip by quickly in order, making
something look like it is moving. A rate is a ratio that compares two
quantities having different units. So, for animation, the number of
pictures that go by in a second is called the frame rate, or “fps.” Two
different frame rates are shown below.
pictures
= 60
1 second
60 fps
One second
pictures
= 24
1 second
MATH TERMS
Rate: A ratio that compares two
quantities with different units.
rate: miles 
→ 110 miles
hour
2 hours
cost
rate:

→ $3.18
ounces
12 ounces
Math Tip
Rates written with a 1 as the
second term are called unit rates.
© 2014 College Board. All rights reserved.
24 fps
Example A
a. Reason quantitatively. If a swimming fish is filmed at 120 frames
in one second, there are 120 photos of the fish. If you played the film
at 10 frames per second, how long would the film play?
rite and solve an equation using the play rate and s, the length of
W
the film in seconds.
number of photos
= play rate× number of seconds
1 second
120 = 10 ×s
1 sec 1 sec
120 = 10s
120 = 10s
10
10
12 = s
Solution: The film would play for 12 seconds.
Activity 18 • Solve Problems Using Ratios 223
Lesson 18-1
Solve Problems Using Ratios
Activity 18
continued
My Notes
b. If Chris films the swimming fish at four times the initial speed of 120
frames in 1 second, he will have more photos of the fish. How many
photos will he have with the faster filming?
Multiply the frame rate times the speed.
Number of photos = frame rate × new speed
120 photos
=
×4
1 second
= 480
Solution: Chris will have 480 photos at the new speed.
Try These A
If a swimming fish is filmed at 100 frames in one second, there are
100 photos of the fish.
a. If you played the film at 20 frames every second, how long would
the film play?
Dimensional analysis is a
problem-solving method that uses
the multiplicative identity property
of one. It states that any number or
expression can be multiplied by
one without changing its value.
A conversion factor is a form of
the value “1” used to change from
one unit to another.
Math Tip
Make sure you keep track of the
units by writing them as you solve
the problem. Then cross out the
units that are the same in the
numerator and denominator.
b. If Chris films the swimming fish at three times the initial speed, he
will have more photos of the fish. How many photos will he have
with the faster filming?
You can use dimensional analysis to solve problems that require one
unit to be converted to another. In Example B, the conversion factor is
found first.
Example B
Make sense of problems. How many frames would be needed for a
1-minute film if it is filmed at 1,000 frames every second?
Step 1:
Determine the number of seconds in 1 minute. This is the
conversion factor.
1 minute = 60 seconds
Step 2:
Multiply 1,000 frames per second by 60 seconds per minute.
1, 000 frames 60 seconds 60, 000 frames seconds
×
=
second
1 minute
1 second minute
60, 000 frames
=
1 minute
Solution: There are 60,000 frames in a 1-minute movie.
Try These B
How many frames would be needed for a 1-minute film if it is filmed at
2,500 frames every second?
224 Unit 4 • Ratios
© 2014 College Board. All rights reserved.
MATH TERMS
Lesson 18-1
Solve Problems Using Ratios
Activity 18
continued
My Notes
Example C
A bean seed is filmed as it grows. It is being filmed at a rate of 1 frame
per minute. Predict how many hours of the bean’s growth will be shown
in 2,910 frames.
Step 1:
Determine the number of frames in 1 hour to be used as the
conversion factor.
1 hour = 60 minutes, or 60 frames in 1 hour
The conversion factor is 1 hour .
60 frames
Step 2:
© 2014 College Board. All rights reserved.
Step 3:
Multiply and cross out the units that are the same in the
numerator and denominator.
2, 910 frames hours
2, 910 frames
× 1 hour =
film
60 frames
60 frames film
2, 910 frames
=
60 film
Math Tip
When finding the conversion
factor, think about multiplying by
one.
Divide 2,910 by 60 and label the solution.
2, 910 hours
= 48.5 hours per film
60 film
Solution: 2,910 frames will produce a 48.5-hour movie of the bean’s
growth.
Try These C
A rock candy crystal is filmed as it grows from a sugar solution. It is
being filmed at a rate of 1 frame per hour. Predict how many days of
the candy’s growth will be shown in 840 frames.
Activity 18 • Solve Problems Using Ratios 225
Lesson 18-1
Solve Problems Using Ratios
Activity 18
continued
My Notes
Check Your Understanding
1. Construct viable arguments. Explain how determining the
solution for Try This C was different from determining the solution
for Try This B.
2. Explain the process you use to determine how many centimeters of
film are in 7 meters of film.
3. A package of film weighs 28 4 ounces. What is the weight of the
5
package in pounds?
LESSON 18-1 PRACTICE
5. Chris is wondering how many hours are left until Career Week starts.
It is in 2 1 days.
2
a. What is the conversion factor that will be used to convert days to
hours? b. How many hours are in 2 1 days? Show your work.
2
6. Make sense of problems. Do conversion factors always,
sometimes, or never have a numerator and denominator that are
equivalent? Explain your choice.
7. A flower is filmed as it goes from slowly opening in the morning to
closing up at night. It is being filmed at a rate of 1 frame per
30 seconds. Predict how many frames of the flower’s blooming will
be shown during 14 hours of daylight.
226 Unit 4 • Ratios
© 2014 College Board. All rights reserved.
4. Chris found out that animators earn an average salary of $46,885 per
year. He wondered how much an animator earns per month.
a. What is the conversion factor to convert dollars per year to dollars
per month? (Hint: Think about your final answer. Should it be
smaller or larger than the yearly amount?)
b. What is the average monthly salary for an animator? Show your
work.