5-3 Solving Proportions
Learn to solve proportions by using cross
products.
Course 2
5-3 Solving
Insert Lesson
Title Here
Proportions
Vocabulary
cross product
Course 2
5-3 Solving Proportions
The tall stack of Jenga® blocks is
25.8 cm tall. How tall is the shorter
stack of blocks? To find the answer
you will need to solve a proportion.
For two ratios, the product of the numerator
in one ratio and the denominator in the
other is a cross product. If the cross
products of the ratios are equal, then the
ratios form a proportion.
Course 2
5-3 Solving Proportions
2 = 6
5 15
5 · 6 = 30
2 · 15 = 30
CROSS PRODUCT RULE
In the proportion a = c , the cross products,
b
d
a · d and b · c are equal.
You can use the cross product rule to solve
proportions with variables.
Course 2
5-3 Solving Proportions
Additional Example 1: Solving Proportions Using
Cross Products
Use cross products to solve the proportion.
9 = m
15
5
15 · m = 9 · 5
15m = 45
15m = 45
15
15
m=3
Course 2
The cross products are equal.
Multiply.
Divide each side by 15 to
isolate the variable.
5-3 Solving Proportions
1.  Write down the proportion
2.  Cross multiply to find the cross productsmake sure to label
3.  Isolate the variable by doing the inverse
operation on both sides- starting with the
variable side
4.  Draw the answer line
5.  Cross out with a 1 on variable side
6.  Drop down the variable
7.  Solve
8.  Check with a STAR
Course 2
5-3 Insert
Title Here
SolvingLesson
Proportions
Try This: Example 1
Use cross products to solve the proportion.
6 = m
7
14
7 · m = 6 · 14
The cross products are equal.
7m = 84
Multiply.
7m = 84
7
7
Divide each side by 7 to
isolate the variable.
m = 12
Course 2
5-3 Solving Proportions
When setting up a proportion to solve a
problem, use a variable to represent the
number you want to find. In proportions that
include different units of measurement, either
the units in the numerators must be the same
and the units in the denominators must be the
same or the units within each ratio must be
the same.
16 mi = 8 mi
4 hr
x hr
Course 2
16 mi = 4 hr
8 mi
x hr
5-3 Solving Proportions
Additional Example 2: Problem Solving Application
If 3 volumes of Jennifer’s
encyclopedia takes up 4 inches of
space on her shelf, how much space
will she need for all 26 volumes?
1
Understand the Problem
Rewrite the question as a statement.
•  Find the space needed for 26 volumes of
the encyclopedia.
List the important information:
•  3 volumes of the encyclopedia take up 4
inches of space.
Course 2
5-3 Solving Proportions
Additional Example 2 Continued
2
Make a Plan
Set up a proportion using the given
information.
3 volumes = 26 volumes
4 inches
x
Course 2
Let x be the
unknown space.
5-3 Solving Proportions
Additional Example 2 Continued
3
Solve
3 = 26
Write the proportion.
4
x
3 · x = 4 · 26 The cross products are equal.
3x = 104
Multiply.
Divide each side by 3 to isolate
3x = 104
the variable.
3
3
x = 34 2
3
She needs 34 2 inches for all 26 volumes.
3
Course 2
5-3 Solving Proportions
Additional Example 2 Continued
4
Look Back
3 =
4
26
34 23
4 · 26 = 104
3 · 34 23 = 104
The cross products are equal, so 34 23 is the
answer
Course 2
5-3 Solving
Insert Lesson
Proportions
Title Here
Lesson Quiz: Part 1
Use cross products to solve the proportion.
1. 25 = 45 t = 36
t
20
2. x = 19 x = 3
9 57
3. 2 = r
r = 24
3 36
4. n = 28 n = 35
10
8
Course 2
5-3 Solving
Insert Lesson
Proportions
Title Here
Lesson Quiz: Part 2
5. Carmen bought 3 pounds of bananas for $1.08.
June paid $ 1.80 for her purchase of bananas.
If they paid the same price per pound, how
many pounds did June buy?
5 pounds
Course 2