Chapter 7.1 Chapter 7.1 and 7.7 and 7.7 Ratios and Proportions Ratios and Proportions and Scale Models and and Scale Models and Drawings Drawings
Chapter 7.1 and
Chapter 7.1 and
7.77.7
Ratios and Proportions and
Ratios and Proportions and
Scale Models and Drawings
Scale Models and Drawings
Definit
ions
Definit
ions Ratio – a comparison
Ratio – a comparison
of two quantities using
of two quantities using
divisiondivision Proportion – an
Proportion – an equation stating that
equation stating that
two ratios are equal
two ratios are equal
Write and Simplify Ratios
SCHOOL The number of students who participate in sports programs at Central High School is 520. The total number of students in the school is 1850. Find the athlete-to-student ratio to the nearest tenth.To find this ratio, divide the number of athletes by the total number of students.
Answer: The athlete-to-student ratio is 0.3.
A. 0.3
B. 0.5
C. 0.7
D. 0.8
The country with the longest school year is China, with 251 days. Find the ratio of school days to total days in a year for China to the nearest tenth. (Use 365 as the number of days in a year.)
Use Extended Ratios
In ΔEFG, the ratio of the measures of the angles is 5:12:13. Find the measures of the angles.
A. 30, 50, 70
B. 36, 60, 84
C. 45, 60, 75
D. 54, 90, 126
The ratios of the angles in ΔABC is 3:5:7. Find the measure of the angles.
Conce
pt
Conce
pt
Use Cross Products to Solve Proportions
Answer: y = 27.3
Use Cross Products to Solve Proportions
B.
A. b = 0.65
B. b = 4.5
C. b = –14.5
D. b = 147
A.
A. n = 9
B. n = 8.9
C. n = 3
D. n = 1.8
B.
Use Proportions to Make Predictions
PETS Hima randomly surveyed 30 students from her class and found that 18 had a dog or a cat for a pet. If there are 870 students in Hima’s school, predict the total number of students with a dog or a cat.
Reci
pes
Reci
pes
Suppose we are having
Suppose we are having
a class party and Jess
a class party and Jess
volunteers to bring
volunteers to bring guacamole. She has
guacamole. She has
recipe that uses 4
recipe that uses 4 avocadoes to make 10
avocadoes to make 10
servings. How many
servings. How many avocadoes does she
avocadoes does she need to make 25
need to make 25 servings?servings?
Sca
le M
odels
Sca
le M
odels
and D
raw
ings
and D
raw
ings
A scale model or a
A scale model or a scale drawing is an
scale drawing is an object or drawing with
object or drawing with
lengths proportional to
lengths proportional to
the object it
the object it represents. The scale
represents. The scale
of a model or drawing
of a model or drawing
is the ratio of a length
is the ratio of a length
to the model or
to the model or drawing to the actual
drawing to the actual
length of the object
length of the object being modeled or
being modeled or drawn.drawn.
Use a Scale Drawing
MAPS The distance between Boston and Chicago on a map is 9 inches. If the scale of the map is 1 inch: 95 miles, what is the actual distance from Boston to Chicago?
A. 800 miles
B. 900 miles
C. 630 miles
D. 720 miles
MAPS The distance between Cheyenne, WY, and Tulsa, OK, on a map is 8 inches. If the scale of the map is 1 inch : 90 miles, what is the actual distance from Cheyenne to Tulsa?
Find the Scale
A. SCALE MODEL A miniature replica of a fighter jet is 4 inches long. The actual length of the jet is 12.8 yards. What is the scale of the model?
Answer: The scale of the model is 1 in. : 3.2 yd.
Find the Scale
B. SCALE MODEL A miniature replica of a fighter jet is 4 inches long. The actual length of the jet is 12.8 yards. How many times as long as the actual is the model jet?
Answer: The scale factor is 115.2 : 1. That is, the actual jet is 115.2 times as long as the model.
A. 2 in. : 3 yd
B. 1 in. : 3 yd
C. 2 in. : 5 yd
D. 3 in. : 4 yd
A. SCALE MODEL A miniature replica of a fire engine is 9 inches long. The actual length of the fire engine is 13.5 yards. What is the scale of the replica?
A. 48
B. 54
C. 60
D. 63
B. SCALE MODEL A miniature replica of a fire engine is 9 inches long. The actual length of the fire engine is 13.5 yards. How many times as long as the model is the actual fire engine?