MFT
TP
O
Solving Proportions
Using Cross Products
CA Standards
NS 1.3
AF 2.2
Goal: Solve proportions using cross products.
Vocabulary
a
c
In a proportion ]] ]] where bp0 and dp0,
b
d
the cross products are ad and bc.
Cross products:
Cross Products Property
Words The cross products of a proportion are equal .
5
7
15
21
Numbers ]] ]]
a
b
7 + 15 105
5 + 21 105
c
d
Algebra If ]] ]] where b and d are nonzero numbers, then
1
EXAMPLE
ad
bc .
Solving a Proportion Using Cross Products
2
5
x
7
Use the cross products property to solve ]] ]].
The phrase
cross products
comes from the "X"
shape formed by the
diagonal numbers in
a proportion.
x
2
]] ]]
7
5
Write original proportion.
2+7 5x
2+7
5x
Divide each side by 5 .
5
Use cross products property.
5
2.8 x
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Simplify.
Lesson 5.4 • Course 1 Notetaking Guide 113
2
EXAMPLE
Writing and Solving a Proportion
Currency Exchange When Jake visited Canada, he exchanged 10 U.S.
dollars and he received 14 Canadian dollars. Find how many U.S. dollars
he exchanged when he received 35 Canadian dollars.
$10
You can also
find the number
of U.S. dollars
Jake exchanged by
using an equivalent
proportion such as:
14
10
$14
$35
10 + 35 10 + 35
35
= u .
Canadian dollars
14u
Use cross products property.
14u
14
U.S. dollars
u
25 Divide each side by 14 .
14
Simplify.
u
Answer: Jake exchanged 25 U.S. dollars when he received
35 Canadian dollars.
EXAMPLE
3
Multiple Choice Practice
Adam spent a total of $1.50 to play an arcade game. Two quarters
operate the game and each game lasts for 3 minutes. At most,
how many minutes did Adam play the game?
A
1.5 min
B
3 min
C
4 min
D
9 min
Solution
Step 1
Convert the money spent into quarters. Because 1 quarter
equals $.25 , Adam used 1.50 0.25 , or 6 quarters, to
play the game.
Step 2
Write a proportion to find the greatest amount of time t (in
minutes) he played the game.
2
6
Quarters
t
Time
3
2+t 3+6
Use cross products property.
t 9
Simplify.
Answer: At most, Adam played the game for 9 minutes.
The correct answer is D .
114
Lesson 5.4 • Course 1 Notetaking Guide
A
B
C
D
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
4
EXAMPLE
Solve a Multi-Step Problem
Baseball The ratio of left-handed pitchers to right-handed pitchers on
a baseball team is 2 to 5. If the team has 14 pitchers, how many are
left-handed?
Solution
First, determine the ratio of left-handed pitchers to total pitchers.
2
2
2 5
Forevery 7 pitchers, 2 are left-handed.
7
To find the number * of left-handed pitchers, set up a proportion and solve it.
*
2
7
14
2 + 14 2 + 14
7*
left-handed pitchers
total pitchers
Use cross products property.
7*
7
Divide each side by
7 .
7
4 *
Simplify.
Answer: There are 4 left-handed pitchers on the team.
Guided Practice
Solve the following problems.
1. In Example 2, if Jake exchanged 45 U.S. dollars, how many Canadian
dollars would he receive?
$63
Homework
2. A baseball team has a ratio of wins to losses of 5 to 3. If they played
24 games, how many games did they lose?
9
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Lesson 5.4 • Course 1 Notetaking Guide
115