LESSON 7.2 NOTES DAY 1
Writing and Solving Proportions Using Cross Products
Goal: Solve proportions using cross products.
WARM-UP:
A proportion is when you put two ratios equal to one another. Look at each of the following
proportions:
2 6
=
3 9
3 12
=
4 16
1 3
=
9 27
For each of the above proportions, multiply the numerator of the first ratio by the
denominator of the second ratio. Record the answer below the proportion.
For each of the above proportions, multiply the denominator of the first ratio by the
numerator of the second ratio. Record the answer below the proportion.
What do you notice about each pair of answers?
Vocabulary
Proportion
Cross Products Property
Words The cross products of a proportion are ____________________________________.
=
Numbers
=
a
c
=
where b and d are nonzero numbers, then ____________________.
b
d
2
x
=
5
7
The phrase cross
products comes
from the “X” shape
formed by the
diagonal numbers
in a proportion
1
EXAMPLE 1 - Solving a Proportion Using Cross Products
Use the cross products property to solve:
Page
Algebra if
NOW YOU TRY IT:
4 8
1)
=
9 x
2)
7 14
=
8 x
EXAMPLE 2 - Use the Cross Products Property to Decide if Two Ratios Form a Proportion
If two ratios form a proportion, they must be _______________________________.
If two ratios are equal, their ________________________________________ will be equal.
A.
27 351
,
32 416
B.
17 425
,
19 476
c.
1 357
,
9 3213
EXAMPLE 3 - Writing and Solving a Proportion
a. 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.
b. 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?
Now You Try It!
Solve the following problems.
1. 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?
2. Use the Cross Products Property to decide if the following ratios, form a proportion.
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2
15 285
,
33 627
EXAMPLE 4 – Use the Cross Products Property to Solve an Algebraic Proportion
4
3
=
x+2 9
Don’t forget to use the distributive property!
Page
3
Now You Try It!
5
3
=
x+4 9