Page 116 - Math Course 3 (Book 2)

Properties of Proportions

means 4x – 5 –26
Solve = .
The ”inside” values of a proportion. 3 6
4x – 5 –26
mean = Original proportion
3 6
10 : 20 = 2 : 4 (4x – 5)6 = 3(–26) Cross products

24x – 30 = –78 Simplify
extremes means
Extremes
3 21 24x = –48 Add 30 to each side.
5 = 35
x = –2 Divide each side by 24.

Key Concept

Answer –2
Property of Proportions

Words For any numbers a and c and any non- Solve Problems Using Proportions
a c
zero numbers b and d, = if
b d
and only if ad = bc. Example

4 12
Example = if and only if 4 • 15 = 5 • 12.
15
5
TRAINS
A boxcar on a train has a length of 40 feet and
a width of 9 feet. A scale model is made with a
length of 16 inches. Find the width of the model.

Let’s Begin

Solve Proportions by Using Cross Products
Because the scale model of the boxcar and the
Example boxcar are in proportion, you can write a proportion
to show the relationship between their measures.
Since both ratios compare feet to inches, you need
not convert all the lengths to the same unit of
6 9 measure.
Solve = .
18.2 y
6 9 boxcar’s length (ft) boxcar’s width (ft)
=

= . Original proportion model’s length(in.) model’s width(in.)
18.2 y
6y = 18.2 (9) Cross products 40 9
= . Substitution
16 x
6y = 163.8 Multiply. 40x = 16(9) Cross products
y = 27.3 Divide each side by 6. 40x = 144 Multiply.

x = 3.6 Divide each side by 40.
Answer y = 27.3.

The width of the model is 3.6
Answer
inches.

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