132 CHAPTER 2 Linear Equations and Inequalities in One Variable
NOTE If then or This means that the two proportions are
equivalent, and the proportion
can also be written as
Sometimes one form is more convenient to work with than the other.
a
c
=
b
d
1 where c, dZ 02.
a
b
=
c
d
ad=cb, ad= bc.
ac=
bd^ ,
Deciding Whether Proportions Are TrueDecide whether each proportion is trueor false.
(a)
Check to see whether the cross products are equal.
The cross products are equal, so the proportion is true.
(b)
The cross products, and are not equal, so the
proportion is false. NOW TRY
6 # 32 = 192 7 # 30 = 210 ,
6
7
=
30
32
3
4
=
15
20
3 # 20 = 60 4 # 15 = 60
3
4
=
15
20
EXAMPLE 3
Finding an Unknown in a ProportionSolve the proportion
Cross products must be equal.
Multiply.Divide by 9.Check by substituting 35 for xin the proportion. The solution set is {35}.
NOW TRY35 = x
315
9
=
9 x
9
315 = 9 x
5 # 63 = 9 #x
5
9
=
x
63
59 =
x63.
EXAMPLE 4
Solve for x.NOW TRY
EXERCISE 3
Decide whether each propor-
tion is trueor false.
(a) (b)
4
13
=
16
52
1
3
=
33
100
NOW TRY
EXERCISE 4
Solve the proportion.
9
7=
x
56NOW TRY ANSWERS
- (a)false (b)true
- {72}
CAUTION The cross-product method cannot be used directly if there is more
than one term on either side of the equals symbol.
Four numbers are used in a proportion. If any three of these numbers are known,
the fourth can be found.
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