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CF6i - Applications of Proportions
供稿人: Heuring
A ratio is a comparison of two quantities by division.
The ratio of 1 teacher to 24 students can be written as:



In Algebra, we prefer to write ratios as fractions.

A statement that two ratios are equivalent, such as



is called a proportion.

24
1
2       4
3       6
Click OK
or      1:24
=
Cross products, or cross multiplication can be
used to solve for a missing value in a proportion.
Find cross products
Use inverse operations
to solve for x
Simplify
Find the value of x.
(30)(x)
30x
30          30
 2       x
30    675
x = 45
Click OK
=
=
=
(675)(2)
1350
Use cross products to solve the proportions for x.
5x  =
x  =
3       x
5     100
=
Type in your answers
20x  =
x      7.5
8      20
x  =
=
If you got x=60 and x=3, then you were correct.
Solving proportions using cross products is a fairly
easy process. The difficulty arises during the
application with similar shapes.
Similar (~) shapes have exactly the same shape,
but not necessarily the same size.
The corresponding sides of similar shapes are
proportional.
Being able to identify the corresponding sides
will play a vital role in the set up of a proportion.
Click OK
Color coding and placing the shapes in the same
relative position is extremely useful.
Type your answers in
  alphabetical order.
C
A
B
∆ABC ~ ∆DEF
Can you pair the corresponding
side of the given triangles?
AC corresponds to
BC corresponds to
AB corresponds to
F
E
D
Now let's use similar shapes and proportions
to find the length of a missing side.
C
x ft
12 ft
A
B
∆ABC ~ ∆DEF
x ft
8 ft
5
5x = 96
5        5
x
x = 19.2 ft
=
=
 (   )
12 ft
  5 ft
8
(    )
12
F
8 ft
5 ft
E
D
Click OK
Now let's use similar shapes and proportions
to find the length of a missing side.
B
A
x ft
C
6 ft
D
ABCD ~ EFGH
x ft

   ft
Type in your answers
x  =
=
number
E
F
 ft

 ft
2 ft
units
G
4 ft
H
Now lets look at using proportions in a different way:
???
A building has a shadow that is 25 feet long.
A person 6 feet tall cast a shadow that is 1 foot long.
How tall is the building?
25 ft
Type in your answers
6 ft
The building is         ft tall.
1 ft
Begin by setting up your proportion.
Then solve it using cross products.
6 ft
A 6 ft tall tent standing next to a cardboard box
casts a 9 ft shadow. If the cardboard box casts a
shadow that is 6 ft long then how tall is it?
Finally, try the last two problems on your own:
If you answered 150 ft - Congratulations!
9ft
???
Type in your answer
6 ft
Begin by setting up your proportion.
Then solve it using cross products.
The box is       ft tall
A statue that is 12 ft tall cast a shadow that is
15 ft long. Find the length of the shadow that
an 8 ft cardboard box casts.
The shadow if the cardboard box is       ft long.
Begin by drawing a picture that represents the problem.
Then set up your proportion and solve it using cross products.
Type in your answer
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