CROSS PRODUCT PROPERTY OF PROPORTIONS
The product of the extremes equals the product of the means.
a
b
c
d
2
4
Example: 3
6
If , then ad bc.
EXAMPLE
2
2p63p4
Use the Cross Product Property
3
y
5
8
Solve the proportion using the cross product property.
5
3
8
y
Write the original proportion.
Use the cross product property.
3p8yp5
24 5y
Simplify the equation.
24
y
5
5
5
24
3
, which simplifies to .
CHECK ✓ Substituting for y, 24 becomes 3 p 2
4
8
5
Solve by dividing each side by 5.
5
EXAMPLE
Student Help
STUDY TIP
Remember to check
your solution in the
original proportion.
Since Example 3 has
two solutions, you need
to check both of them.
3
Use the Cross Product Property
3
x
x1
4
Solve the proportion .
Write the original proportion.
Use the cross product property.
3
x1
x
4
(3)(4) (x)(x 1)
12 x2 x
Multiply.
Collect terms on one side.
0 x2 x 12
Factor the right-hand side.
0 (x 3)(x 4)
Solve the equation.
x 3 or 4
ANSWER 䊳
The solutions are x 3 and x 4. Check both solutions.
Use the Cross Product Property
Solve the proportion. Check your solutions.
2
5
1. b
2
25
n
2. n
4
p
q
3
x6
3. x
3
x
x 1
4. 4
x
r
s
Consider the equation where p, q, r and s are polynomials and q and s are
restricted so that they do not equal zero. Writing both fractions with a common
ps
qs
qr
qs
denominator leads to , and then to ps qr. This reasoning is the basis for
cross multiplying, a method of solving equations used in Example 4.
634
Chapter 11
Rational Expressions and Equations