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4-3 Solving Proportions
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Simplify the ratios to determine if they
are proportional.
4-3 Solving Proportions
Learn to solve proportions by using cross
products.
4-3 Solving Proportions
In the previous lesson we discussed two ways
to determine if a pair of ratios form a
proportion by:
-Simplifying the ratios
-Finding common denominators
4-3 Solving Proportions
A third and often simpler way to determine if
they form a proportion is to use cross
products.
If the cross products are equal, then the
ratios form a proportion.
4-3 Solving Proportions
2 = 6
5 15
5 · 6 = 30
2 · 15 = 30
4-3 Solving Proportions
Use cross products to solve the proportion.
9 = m
15
5
15 · m = 9 · 5
15m = 45
15m = 45
15
15
m=3
4-3 Solving Proportions
p = 10
6
3
3 = 15
x
30
x = 13
5
20
10 · 6 = 3 · p
15 · x = 3 · 30
5 · 13 = 20 · x
60 = 3p
60 = 3p
3
3
15x = 90
15x = 90
15
15
65 = 20x
65 = 20x
20
20
20 = p
x=6
3.25 = x
4-3 Solving Proportions
It is important to set up proportions correctly.
Each ratio must compare corresponding
quantities in the same order.
Suppose a boat travels 16 miles in 4 hours and
8 miles in x hours at the same speed. Either of
these proportions could represent this
situation.
16 mi = 8 mi
4 hr
x hr
16 mi = 4 hr
8 mi
x hr
4-3 Solving Proportions
Steps
1) Set up a proportion with the same labels
across from each other.
ex: miles
miles
=
hour
hour
2) Fill in the known values
3) Solve using cross products (cross
multiplication)
4-3 Solving Proportions
Example C:
If 3 volumes of Jennifer’s encyclopedias takes
up 4 inches of space on her shelf, how much
space will she need for all 26 volumes?
3 volumes = 26 volumes
4 inches
x
volumes
inches
3 = 26
4
x
She needs 34 2 inches for all 26 volumes.
3
4-3 Solving Proportions
John filled his new radiator with 6 pints of
coolant, which is the 10 inch mark. How many
pints of coolant would be needed to fill the
radiator to the 25 inch level?
6 pints
10 inches
=
p
25 inches
pints
inches
6 = p
10 25
15 pints of coolant will fill the radiator to the 25 inch level.
4-3 Solving Proportions
Lesson Quiz: Part I
Use cross products to solve the proportion.
1. 25 = 45
t
20
2. x = 19
9 57
3. 2 = r
3 36
4. n = 28
10
8
t = 36
x=3
r = 24
n = 35
4-3 Solving Proportions
Lesson Quiz: Part II
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
4-3 Solving Proportions
Lesson Quiz for Student Response Systems
1. Use cross products to solve the proportion.
24 = 48
16
t
A. t = 16
B. t = 24
C. t = 32
D. t = 36
4-3 Solving Proportions
Lesson Quiz for Student Response Systems
2. Use cross products to solve the proportion.
y = 21
16
84
A. y = 2
B. y = 4
C. y = 8
D. y = 16
4-3 Solving Proportions
Lesson Quiz for Student Response Systems
3. Use cross products to solve the proportion.
4 = r
5
25
A. r = 20
B. r = 15
C. r = 10
D. r = 5
4-3 Solving Proportions
Lesson Quiz for Student Response Systems
4. Use cross products to solve the proportion.
n = 21
16
12
A. n = 21
B. n = 28
C. n = 32
D. n = 36
4-3 Solving Proportions
Lesson Quiz for Student Response Systems
5. If you put an object that has a mass of 25
grams on one side of the balance scale, you
would have to put 55 paper clips on the
other side to balance the weight. How
many paper clips would balance the weight
of a 30-gram object?
A. 55 paper clips
B. 58 paper clips
C. 60 paper clips
D. 66 paper clips