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Math 84
Activity # 20
Your Name: _______________________
“Proportion”
Remember:
equal.
A proportion is a mathematical statement that two ratios or rates are
Example of a true proportion:
4 24
We know this because 4 x 18 = 3 x 24 or … 72 = 72
=
3 18
Remember the cross products rule;
If
a c
= , then ad = bc !
b d
Task 1: In problems 1 – 3, determine whether the proportion is true or false.
1)
13
104
=
7
56
2)
30 miles
18 miles
=
35 days
42 days
3)
$75
$3
=
1000 minutes
40 minutes
Solve for x.
4)
70
15
=
x
21
Using a proportion equation:
5)
6
15
=
14
x
6)
0.9
x
=
1.6
0.5
a c
= , solve the following word problems.
b d
7) If a 10,000 gallon swimming pool requires 4 ounces of a chemical, then how many ounces of
the chemical would be required for a 200 gallon pool?
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8) If eight trash bags last for thirty days, then twenty-eight trash bags will last for how many
days?
9) If four out of ten people vote, then in a town with two hundred thousand people, how many
will vote?
10) Write a word problem that might come up in your everyday life. Solve the problem and pass
right for your partner to solve (don’t let them see the answer!)
Task 2: Try the following exercises in writing a proportion.
Write a proportion from each set of numbers. Only use 4 numbers from each set of numbers.
1. 2, 10, 8, 7, 28
Ans:
3. 1, 8, 4, 2, 10
Ans:
5. 52, 12, 6, 26
2. 20, 18, 30, 27
Ans:
4. 7, 3, 21, 9, 32
Ans:
6. 24, 15, 16, 10
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Ans:
Ans:
Another way to check if a proportion is true, is to use “cross-products” or “cross multiplication.” By multiplying the
diagonals of the proportion, these cross-products must be equal. Example: In
(products of the diagonals) are,
20
4
= , the cross products
25
5
20 ⋅ 5 and 25 ⋅ 4 . Do you see where these products come from in the proportion?
And are these cross-products equal? Does
20 ⋅ 5 = 25 ⋅ 4 ?
TASK 3: Use Cross-Products/Cross-Multiplication, to verify if the following proportions are true.
If
1)
6
2
=
9
3
True or False?
4
16
4)
=
8
28
a
c
= , then a ⋅ d = b ⋅ c
b
d
2)
15
75
=
2
10
True or False?
0.5
56.25
5)
=
0.2
2.25
3)
1.3
0.975
=
4
3
True or False?
1
3
6) 2 =
6
36
True or False?
True or False?
True or False?
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Task 4: Solving Proportions: We can also use the Cross-Products Rule (C.P.R.) to find a missing
number in a proportion. Solve the following proportions and then check the solution in the
original statement.
7)
15 75
=
2
x
8)
3 p + 15 5
=
2
3
10)
4 16
=
b 28
11)
0.5
x
=
0.2 2.25
9)
c +1 1
=
5
5
3
x
12)
= 4
7
1
1
4
8
10
3
13) Sam drove 320 miles in 2.5 hours, how long will it take to drive 500 at the same rate
(speed)?
14)
12
18
4
y
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16
x
The triangles are similar. Solve for x and y.