Lesson 37 - the Home Page for Voyager2.DVC.edu.

Transcription

Free Pre-Algebra
Lesson 37 ! page 1
Lesson 37
Scale and Proportion
Ratios and rates are a powerful way to compare data. Comparing and calculating with ratios and rates is one of the most
common and useful ways we think mathematically every day. When ratios are equal, we say they are in proportion. The
most visual way to think about proportion is seeing the same shape in different sizes.
Similar Figures
Scale models are interesting because they look “just like” the real
thing except for the size. The way to achieve that is to keep the
proportions – the ratios of measurements – the same in the
model as in the original item.
Consider the drawings on graph paper below.
1
2
2
4
These figures are similar.
Each of the sides in the
larger figure is twice the
length of the
corresponding side in the
smaller figure. The ratio
1/2 is the same as the ratio
2/4. Check that this is true
for any two sides.
The shapes of the figures
look the same. Only the
size is different.
These figures are not
similar. You can see that
the shapes are slightly
different. The larger figure
seems to have a relatively
shorter, thinner base
compared to the smaller
figure.
The corresponding sides
are not in proportion, since
the ratio 1/2 is not the same
as the ratio 2/3.
© 2010 Cheryl Wilcox
Fascination with Scale
People seem to enjoy things in unusual sizes.
Free Pre-Algebra
Lesson 37 ! page 2
Photographs and photocopies are easily re-sized with lenses or
digital computations. When you re-size an image with a computer
program, you are usually given a default choice to “maintain
aspect ratio”. That means that when you resize one side, the
other stays in the same proportion as in the original. If you do not
choose this option, the photo will appear distorted.
Art Glossary and Vocabulary: Grid Enlarging
from http://www.bluemoonwebdesign.com/art-glossary-2.asp
A grid is made over the smaller image. By copying the
parts of the picture square by square into a larger grid,
the picture is enlarged (by hand) while keeping the
proportions constant.
Largest carp ever caught! 256 pounds.
Photo: width 1.875 inches x length 3 inches. Ratio of width to length 1.875 / 3 = 0.625.
The photo was reduced in size but the ratio of width to length
is still the same.
Only the width of this photo was reduced, causing the fish
to appear relatively longer and thinner.
Width 1 inch x Length 1.6 inches.
Ratio of width to length is 1 / 1.6 = 0.625.
Width 1 inch x Length 3 inches.
Ratio of width to length is 1 / 3 = 0.333…
Example: Find the ratio of the shorter side to the longer side for each rectangle. Which rectangles are similar?
This rectangle is similar to
the first rectangle.
1.3 inches by 1.95 inches
1.5 inches x 1.5 inches
0.8 inches by 1.2 inches
0.77 inches x 1.5 inches
Ratio approx 0.67
Ratio 1
Ratio approx 0.67
Ratio approx 0.51
Free Pre-Algebra
Lesson 37 ! page 3
(Almost) Every Which Way
An interesting thing about equal ratios is that you can set them up and compare in a variety of ways. Suppose we have the
two similar rectangles below.
You can organize the information about the rectangles into a table, which turns out to be very helpful.
CM
BLUE
PINK
LENGTH
2
3
WIDTH
1
1.5
To compare the length and width of each rectangle, you use the columns of the table:
length 2
3
= =
=2
width 1 1.5
The length is twice the width in each
rectangle.
width 1 1.5
= =
= 0.5
length 2
3
The width is 1/2 the length in each
rectangle.
The rectangles are similar so the column ratios and their reciprocals are equal. The ratio of length to width for both
rectangles is 2, and the ratio of width to length is the same ratio upside down, the reciprocal, 1/2 = 0.5. These ratios
compare the length to the width within each rectangle.
The rectangles are similar so it is also true that the ratios of corresponding sides of the rectangles are equal. The ratios are
in the rows of the table.
blue 2
1
= =
= 0.6
pink 3 1.5
pink 3 1.5
= =
= 1.5
blue 2
1
The sides of the blue rectangle are 2/3
of the corresponding sides of the pink
rectangle.
The sides of the pink rectangle are 1.5
times the corresponding sides of the
blue rectangle.
These ratios compare the side of one triangle to the side of the other. The sides of the pink rectangle are 1.5 times the sides
of the blue rectangle. However, be careful about saying that the pink rectangle is 1.5 times as big as the blue rectangle,
because the ratio of areas is NOT the same as the ratio of sides.
So you can compare the ratios of rows or columns in the table. How about along the diagonal?
The numbers in the diagonal do not form equal ratios. Instead they form equal products,
called cross-products.
2 • 1.5 = 3 • 1 = 3
You can see that the cross products of all the different ratios for the table are the same.
People often use the cross product to check that two ratios are equal without doing division.
Free Pre-Algebra
Lesson 37 ! page 4
CM checkGREEN
ORANGE
Example: Organize the information from the triangles into a table,
that the cross-products
are equal, and
write the requested ratios.
SIDE A
SIDE C the information into a table.
a. Organize
CM
b. Check that the cross products are equal. Are the
triangles similar?
GREEN
ORANGE
SIDE A
3
0.6
SIDE C
5
1
c. What is the ratio of side a to side c in each triangle?
3
= 0.6
5
0.6
= 0.6
1
d. What is the ratio of the sides of the green triangle to
the corresponding sides of the orange triangle?
3•1=3
3
=5
0.6
5 • 0.6 = 3
Cross products are equal, therefore the
triangles are similar.
5
=5
1
This means that the sides of the green triangle are 5 times
as long as the sides of the orange triangle.
Since we know the triangles are similar, we can find the length of a missing side from the ratios.
Example: Find the length of side b of the orange triangle in the problem above.
1 Make a table that includes the
missing side (use a variable).
CM
2 Use the cross-products to write an
equation.
GREEN ORANGE
SIDE B
4
b
SIDE C
5
1
4 • 1= 5 • b
3 Simplify and solve the equation.
5b = 4
5b / 5 = 4 / 5
4
b = = 0.8
5
Side b of the orange triangle
is 0.8 cm long.
Example: The rectangles shown are similar. Fill in the table and find the length of the larger rectangle.
a. Fill in the table. Use a variable
for the unknown side.
LARGE SMALL
LENGTH
WIDTH
L
1 1 /4
2
3 /4
b. Find the length of the larger rectangle.
3
1 2 5 5
L = 2•1 = •
=
4
4 1 4 2
2
2
3
5
L=
4
2
4 3
5 4
• L= •
3 4
2 3
10
1
L=
= 3 inches
3
3
Free Pre-Algebra
Lesson 37 ! page 5
Scale
Models are usually made according to a scale, which is a ratio that compares the sizes of the model to the original. For
example, the O Scale for model railroads is written 1:48, read “1 to 48.” (The colon : is in place of the fraction bar / as an
alternative way to write a ratio.) The ratio means that 1 inch in the model corresponds to 48 inches on the original train.
Model makers often need to figure out measurements in their scale corresponding to measurements of the original object
using the scale, but the scales are usually designed to make such conversions very easy.
For example, dollhouses often come in a 1:12 scale, meaning that 1 inch in
the dollhouse corresponds to 12 inches (1 foot) in the original house. A scale
is written as a ratio of like units, so the scale 1:12 means that something
measuring 1 inch in the dollhouse measures 12 inches in a real house.
Since 12 inches is 1 foot, the choice of scale allows us to simply change the
unit of measurement to find the corresponding length.
If a real piano keyboard is 21/2 feet above the floor, the dollhouse piano
keyboard will be 21/2 inches above the floor. If the dollhouse bookshelf is 6
inches tall, the corresponding real bookshelf is 6 feet tall.
Architects working in metric units may use a scale 1:100 for plans, because there are 100 cm in 1 m. That way distances
measuring 1 m on the construction site will be represented by 1 cm on the architectural plans, and conversions consist only
of changing the name of the unit of measurement.
Sometimes the scale is not exactly a change of unit, but requires slightly more work.
Example: A model airplane is made in a 1:48 scale. If the original aircraft had a wing span of 37 feet, what is the
wingspan of the model?
The 1:48 scale represents a ratio of like units.
We could make a table:
SCALE MEASUREMENT
MODEL
1
x feet
ORIGINAL
48
37 feet
Solving the cross-product equation:
1• 37 = 48x
48x = 37
48x / 48 = 37 / 48
x ! 0.77 feet
As a model-builder, this answer might not be very helpful. It would be better in inches.
0.77 feet 12 inches
•
= 9.25 inches
1
1 foot
SCALE MEASUREMENT
MODEL
1
x feet
If you’re doing many of these conversions, you’d probably set it up with different units in the scale. Since 48 inches is the
same
as 4 feet, you48
could write37
model
measurements in inches and original measurements in feet. Then solving the crossORIGINAL
feet
product equation would give your answer directly in inches.
SCALE
MEASUREMENT
MODEL
1 inch
x inches
ORIGINAL
4 feet
37 feet
1• 37 = 4x
4x = 37
4x / 4 = 37 / 4
x = 9.25 inches
Free Pre-Algebra
Lesson 37 ! page 6
Maps and Scale
To the right, see part of a map of Yosemite National Park. The map
has a scale, showing distances on the map corresponding to real
distances that visitors would hike or drive. The ruler below shows
that 2 inches on the map (at the size shown) corresponds to
5 miles of real distance.
Information Station
h ic
To estimate distances on the map, people usually match some
distance on the scale to a length on a finger, then use that length to
measure out curvy roads or rivers. To be more precise, they might
calculate with the units included, as the model builders did above.
Big
Oa
le t
raffic
lumne
Tuo
F o rk
Tioga Road closed
November to May
east of this point
TUOLUMNE
GROVE
k
However, to a geographer, the scale of the map should properly be
written in like units (so that the units cancel from the ratio). So to
find the scale of the map, we’d convert 5 miles to inches.
120
River
ad
Ro
Big Oak Flat Entrance
th
W
Sou
Old
B ig
Hodgdon clos
Oa
ed
k F
Meadow
to
lat
ve
Fl a t
Road
Crane Flat
MERCED
GROVE
0
0
5 Kilometers
1
1
5 Miles
5 miles 5280 feet 12 inches
•
•
= 316,800 inches
1
1 mile
1 foot
The ratio of map distance to real distance is
1
2 inches
316,800 inches
=
1
158,400
The scale is 1:158,400, meaning that distances in the
park are 158,400 times as great as they are on the
map.
158,400
Map Scales from a Geography Syllabus
http://krygier.owu.edu/krygier_html/geog_222/geog_222_lo/geog_2
22_lo04.html
Example: Show that the ratio of inches to miles and cm to
km for the first map are the same as the representative
fraction given for that map.
a. Convert 1,485 miles to inches. (63,360 inches = 1 mile)
1,485 miles 63,360 inches
•
1
1 mile
= 94,089,600 inches
When rounded, the ratio is about 1 / 94,000,000.
b. Convert 940 km to cm. (100,000 cm = 1 km)
940 km 100,000 cm
•
1
1 km
= 94,000,000 cm
The ratio is 1 / 94,000,000.
Note that it’s far easier to convert the version in metric units, since in that system conversions are based on powers of ten.
!
Free Pre-Algebra
Lesson 37 ! page 7
Lesson 37: Scale and Proportion
Worksheet
Name ________________________________________
1. Fill in the table with the
information from the rectangles.
2. Use the cross-products to check whether or not the
rectangles are similar.
LARGE SMALL
LENGTH
WIDTH
3. What is the ratio of length to width in the two rectangles?
4. What is the ratio of the side of the large rectangle to the
corresponding side of the small rectangle?
Fill in the blank:
Fill in the blank:
The length is ______ times the width in both rectangles.
The sides of the large rectangle are _______ times the
corresponding sides of the small rectangle.
5. Use the steps following to verify that the triangles are
similar, and to find side c of the larger triangle.
a. Fill in the table for sides a and b and check cross products
37 worksheet
stuffare similar.
in order to verify that
the triangles
LARGE SMALL
37 worksheet stuff
SIDE A
LARGE SMALL
SIDE B
SIDE A
LARGE SMALL
SIDE B
LARGE SMALL
SIDE A 1.25
0.5
b. Fill in the table for sides a and c and use cross products
SIDE
3
1.2
to write an equation
forBthe missing
side.
SIDE A
1.25
0.5
SIDE B
3
1.2
c. Solve the equation to find the side c.
LARGE SMALL
SIDE A
LARGE SMALL
SIDE C
SIDE A
LARGE SMALL
SIDE C
LARGE SMALL
SIDE A
1.25
0.5
SIDE C
C
1.3
SIDE A
1.25
0.5
SIDE C
C
1.3
SCALE CONVERSION
SCALE CONVERSION
MODEL
1
REAL
87
1.97
SIDE A 1.25
0.5
SIDE A LARGE SMALL
SIDE A
SIDE C
C
1.3
SIDEB AC
SIDE
SIDE C
Free Pre-Algebra
Lesson 37 ! page 8
LARGE SMALL
LARGE SMALL
6. A typical H0
(1:87)
railroad0.5
engine is 1.97 inches tall, and 3.94 to 11.81 inchesSCALE
long. CONVERSION
SIDE A model
1.25
LARGE
SMALL
SIDE A 1.25
0.5
(http://en.wikipedia.org/wiki/Rail_transport_modelling)
MODEL
1
1.97
SIDE AC 1.25
C
1.3
0.5
SIDE B
3
1.2
REAL
873.94 inches correspond?
a. How tall is the real engine being modeled?
b. To what real
length does
SIDE C
C
1.3
LARGE SMALL
SCALE CONVERSION
SIDE A
MODEL SCALE
1
1.97
CONVERSION
SIDE C
REAL
87
MODEL
1
1.97
REAL LARGE
87 SMALL
SCALE CONVERSION
SIDE A 1.25
0.5
MODEL SCALE
1
3.94
CONVERSION
SIDE C
C
1.3
REAL
87
MODEL
1
3.94
c. How many feet of track correspond to 5280 feet
REAL
(1 mile) for real
trains? 87
SCALE CONVERSION
CONVERSION
SCALE
MODEL SCALE
11.81
CONVERSION
MODEL
11
1.97
REAL
MODEL
REAL
REAL
1
8787
87
1
REAL
87
3.94
SCALE CONVERSION
7. a. A mapMODEL
legend shows
1 a line 7/8 inch long to represent
2000 feet. How many feet are represented by a line 1 inch
REAL
87
5280
long?
MAP
MODEL
1
REAL
87
3.94
SCALE CONVERSION
MODEL
1
REAL
87
11.81
5280
SCALE CONVERSION
MODEL
SCALE CONVERSION
SCALE
CONVERSION
7/8 inch
1 inch
REAL 2000 feet x feet
HO Scale GE 44-ton switcher made by Bachmann,
shown with a pencil for size.
b. What is the scale of the map as a ratio of like units?
c. The real distances are about ____________ times as far
as the distances shown on the map.
(Round to the nearest thousand.)
LARGE SMALL
Free Pre-Algebra
SIDE A
1.25
0.5
Lesson 37 ! page 9
SIDE B
3
1.2
8. A Google map showing part of Pleasant Hill, California. The map scale is in the lower left hand corner.
LARGE SMALL
SIDE A
SIDE C
LARGE SMALL
SIDE A
1.25
0.5
SIDE C
C
1.3
SCALE CONVERSION
MODEL
1
REAL
87
1.97
SCALE CONVERSION
a. Measure the scale with your finger and estimate the
length and width of the (real) Diablo Valley College
campus.
MODEL
1
REAL
87
SCALE CONVERSION
c. If the lengthMODEL
on the map representing
2000 feet is 7/8 inch long,
1
how many inches on the map represents a distance of 5280 feet
REAL
87
5280
(1 mile)?
MAP
b. What is the approximate real length of Taylor Blvd
from Pleasant Hill Road to Contra Costa Blvd?
3.94
SCALE
CONVERSION
7/8 inch
x inches
REAL 2000 feet 5280 feet
Free Pre-Algebra
Lesson 37 ! page 10
Homework 37A
c
Name _______________________________________
A = !r 2
4 3
!r
3
Formulas for Circles and Spheres:
C = 2!r
1. Find the circumference and area of a circle with radius
12.5 miles. Round to the nearest tenth.
2. Find the volume of a sphere with radius 12.5 miles. Round
to the nearest whole number.
3. Solve the equation.
4. If a circle has circumference 8.75 inches, what is the
radius, to the nearest tenth?
0.7x ! 0.5 = 1.95
5. Use the table to make the requested comparisons.
1965
U.S. Population
V=
b. Write one or more sentences comparing the data.
2005
195 million 296 million
Number of Smokers
a. Find the rate comparing smokers to total population for
1965 and 2005. Write as a decimal rounded to the nearest
hundredth.
6. Change the numbers to scientific notation.
8. a. Write the number in standard form.
a. 78,999,000,000,000
They were charging $2.8 million for that
house.
b. 715,000,000,000,000,000
7. Change to standard notation.
a. 2.13 x
1014
b. 2.7 x 108
b. Write with a decimal point and place value name.
This house was only $1,400,000.
Free Pre-Algebra
Lesson 37 ! page 11
LARGE SMALL
LARGE SMALL
9. The rectangles are similar. Find the
of the smaller
L width
3.75
1.5
rectangle.
W 1.25
W
L
3.75
1.5
10. a. What is the ratio of length to width for each of the
W in #9?
1.25
W
rectangles
LARGE SMALL
LARGE SMALL
L
W
L
b. Fill in the blank:
W
The length is ______ times the width in both rectangles.
c. What is the ratio of
the sidesCONV.
of the large rectangle to the
SCALE
corresponding sides of the small rectangle?
SCALE CONV.
MODEL
1
x feet
MODEL
1
x feet
REAL
180 311.5 feet
REAL
311.5 feet
d. Fill in the blank: SCALE CONV.
L
3.75
1.5
of the larger1rectangle are ______ times the
SCALE CONV.The sidesMODEL
corresponding sides of the smaller rectangle.
W 1.25
W MODEL
1
REAL
180
REAL
180
11. Pictured below is the Revell 1:180
USS Lionfish
12. A map legend shows that a length of 11/4 inches on the
LARGE
SMALL
Submarine model.
map correspondsSCALE
to a distance of CONVERSION
500 miles.
L
SCALE
CONVERSION
The distance
Oakland, California
and Chicago,
MAPbetween
5/4 inches
45/16 inches
5/ inches on the map. About how many
Illinois
is
about
4
16
5
W
MAP 5/4 inches
4 /16 inches
REAL
miles
x miles
miles apart
are the500
cities?
REAL 500 miles
x miles
SCALE CONV.
SCALE
CONVERSION
MODEL
1
x feet SCALE
CONVERSION
MAP 5/4 inches
a. The actual length of the submarine is 311.5 feet. What is
REAL
180
311.5
feet
MAP
5/4 inches
the length of the model, in feet?
REAL 500 miles
REAL 500 miles
SCALE CONV.
LARGE SMALL
MODEL
180
1
REAL
180
SCALE
CONVERSION
MAP
5/4 inches
45/16 inches
REAL
500 miles
x miles
b. What is the length of
the model in inches?
SCALE
CONVERSION
MAP
5/4 inches
REAL
500 miles
Free Pre-Algebra
Lesson 37 ! page 12
Homework 37A Answers
12.5 miles. Round to the nearest tenth.
(
)
C = 2! 12.5 miles " 78.5 miles
(
A = ! 12.5 miles
)
2
" 490.9 square miles
V=
4 3
!r
3
2. Find the volume of a sphere with radius 12.5 miles.
Round to the nearest whole number.
V=
(
4
! 12.5 miles
3
)
3
" 8181 cubic miles
4. If a circle has circumference 8.75 inches, what is the
0.7x ! 0.5 = 1.95
0.7x ! 0.5 = 1.95 0.7x ! 0.5 + 0.5 = 1.95 + 0.5
0.7x = 2.45 0.7x / 0.7 = 2.45 / 0.7
x = 3.5
1965
U.S. Population
A = !r 2
C = 2!r
2005
Number of Smokers
8.75 inches = 2!r
2!r = 8.75
2!r / (2! ) = 8.75 / (2! )
r " 1.4 inches
b. Write one or more sentences comparing the data.
Although the number of smokers has
increased since 1965, the total population
has increased even more. Smokers are a
smaller ratio of total population in 2005 than
they were in 1965.
a. Find the rate comparing smokers to total population for
1965 and 2005. Write as a decimal rounded to the nearest
hundredth.
1965: 48/195 is about 0.25
2005: 50/296 is about 0.17
a. 78,999,000,000,000
They were charging $2.8 million for that
house.
7.8999 x 1013
b. 715,000,000,000,000,000
7.15 x 1017
a. 2.13 x
1014
b. 2.7 x 108
213,000,000,000,000
270,000,000
$2,800,000
This house was only $1,400,000.
$1.4 million
Free Pre-Algebra
Lesson 37 ! page 13
9. The rectangles are similar. Find the width of the smaller
rectangle.
rectangles in #9?
3.75
1.25
LARGE = SMALL
3
LARGE SMALL
L
3.75
1.5
W
1.25
W
LARGE SMALL
3.75W = (1.5)(1.25)
L
3.75W = 1.875
3.75W / 3.75 = 1.875 / 3.75
W
W = 0.5
The width is 0.5 feet.
11. Pictured below is the Revell 1:180 USS Lionfish
LARGE SMALL
Submarine model.
L
3.75
1.5
W
W
1.25
L
3.75
1.5
W 1.25
W
The length is __3__ times the width in both rectangles.
c. What is the LARGE
ratio of theSMALL
sides of the large rectangle to the
L
W
3.75
= 2.5
1.5
map corresponds toSCALE
a distanceCONV.
of 500 miles.
The distance
between Oakland,
California and Chicago,
MODEL
1
Illinois is about 45/16 inches on the map. About how many
REAL
180
miles apart
are the cities?
SCALE
REAL
1
x feet
180
311.5 feet
SCALE CONV.
180x = 311.5
180x / 180 = 311.5 / 180
MODEL
1
x ! 1.73 feet
REAL
5/4 inches
45/16 inches
REAL
500 miles
x miles
SCALE
CONVERSION
! 69 $
5
8625
MAP
x = # 5/4&inches
500 =
4
4
" 16 %
REAL
(
)
500 miles
5
8625
4 5
8625 4
x=
• x=
•
4
4
5 4
4
5
x = 1725
180
b. What is the length of the model in inches?
1.73 feet 12 inches
•
= 20.76 inches
1
1 foot
CONVERSION
MAP
SCALE CONV.
MODEL
1.25
= 2.5
0.5
d. Fill in the blank: SCALE CONV.
The sidesMODEL
of the larger 1rectangle xarefeet
__2.5__ times the
corresponding sides of the smaller rectangle.
REAL
180 311.5 feet
LARGE SMALL
L
a. The actual length of the submarine is 311.5 feet. What is
W model, in feet?
the length of the
1.5
=3
0.5
Oakland and Chicago are
about 1,725 miles apart.
Free Pre-Algebra
Lesson 37 ! page 14a
Homework 37B
Name _____________________________________
C = 2!r
A = !r 2
V=
4 3
!r
3
7.3 m. Round to the nearest tenth.
2. Find the volume of a sphere with radius 7.3 m. Round to
the nearest whole number.
4. If a circle has circumference 45 inches, what is the
1.7x + 8.1= 16.6
Median Home Prices by state,
Adjusted for inflation to equivalent 2000 dollars.
1980
2000
CALIFORNIA $249,800
$211,500
COLORADO $105,700
$166,600
http://www.census.gov/hhes/www/housing/census/historic/val
ues.html
Find the difference in home prices from 1980 to 2000 in
California and in Colorado, and compare in one or more
sentences.
a. 35,087,000,000
The cost of the cleanup is estimated at
$7.2 billion.
b. 882,993,000,000,000
a. 4.09 x
1010
b. 1.15 x 108
There are over 9,500,000,000,000 reasons
why I shouldn’t do that.
Free Pre-Algebra
Lesson 37 ! page 15a
9. The rectangles are similar. Find the width of the smaller
rectangle.
SMALL
LARGE
L
The length is _______ times the width in both rectangles.
W
c. What is the ratio of the sides of the large rectangle to the
SCALE
MODEL
REAL
SCALE
CONVERSION
SMALL LARGE
d. Fill in the blank:
L
The sides of the larger rectangle are about ______ times the
correspondingWsides of the smaller rectangle.
CONVERSION
11. Pictured below is the RevellMAP
1:535 USS Missouri
Battleship model.
REAL
SMALL
SCALE of 10
CONVERSION
map corresponds to a distance
miles.
CM
SMALL
LARGE
SIDE A
LARGE
SIDE C
1.3
2.86
1.9
c
L
a. The actualWlength of the battleship is 887.2 feet. What is
SMALL LARGE
CM
the length of the model, in feet?
SIDE A
1.3
2.86
SCALE SIDE
CONVERSION
B
2.1
4.62
MODEL
REAL
SCALE
CONVERSION
MAP
b. What is the length of the model in inches?
REAL
SMALL
LARGE
SIDE A
1.3
2.86
SIDE C
1.9
c
CM
SMALL
CM
SIDE A
1.3
SIDE B
2.1
rectangles in #9?
LARGE
2.86
4.62
The distance MODEL
between Pleasant Hill, California and Davis,
CA is about 33/4 inches on the map. About how many miles
REAL
apart are the cities?
SCALE
CONVERSION
MAP
REAL
SMALL
LARGE
SIDE A
1.3
2.86
SIDE C
1.9
c
SMALL
LARGE
SIDE A
1.3
2.86
SIDE B
2.1
4.62
CM
CM

Lesson 37 - the Home Page for Voyager2.DVC.edu.

Transcription

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