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?