Objective 3: DETERMINE IF A PROPORTION IS TRUE
A proportion is made when two rates or two ratios are set equal to each other.
Ex. 1
100 miles
20 miles
=
5 hours
1 hour
Ex. 2
100 miles
20 miles
=
15 miles
3 miles
(Two Rates)
or
100
20
=
15
3
(Two Ratios)
To determine if the proportion is true:
1. Be sure the units in the numerators are the same and the units in the denominators
are the same.
2. Reduce the fractions to their lowest terms.
3. If the fractions are the same, the proportion is true.
Ex. 3
100 miles
50 miles
=
4 gallons
2 gallons
1. The units in the numerators are the same (miles).
The units in the denominators are the same (gallons).
2. The fractions reduce to
25 miles
25 miles
=
1 gallon
1 gallon
3. The fractions are the same, the proportion is true.
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Another method can be used to determine if a proportion is true. This method uses
multiplication of "cross products".
Ex. 4
3 6
=
4 8
Using "cross products":
Ex. 5
(Note:
6
3
reduces to
which makes the proportion true)
4
8
3
6
=
4
8
3 • 8 = 6• 4
24 = 24
True
so: The proportion is true
5 9
=
6 8
Using "cross products";
5
9
=
6
8
5• 8 = 6• 9
40 = 54
False
so: The proportion is false
----------------------------------------------------------------------------------------------------PRACTICE: DETERMINE IF THE PROPORTIONS ARE TRUE OR FALSE
1.
6
4
=
12 8
2.
5
9
=
3 15
3.
3 7
=
5 8
4.
5
20
=
12 48
5.
6 8
=
5 7
6.
3
9
=
4 12
-------------------------------------------------------------------------------------------------------
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Objective 4: FIND AN UNKNOWN IN A GIVEN PROPORTION
If one of the numbers in a proportion is not known, it is necessary to solve the
proportion.
To solve a proportion, find a number to replace the unknown.
2 8
=
7 n
Ex. 1 Solve for n:
2• n = 7• 8
2 • n = 56
Step 1: Find the "cross products"
28
2 56
Step 2: Divide the 56 by the 2
n = 28
Always divide the number that is alone by the number that is next
to the letter.
Think about the relationship between multiplication and division:
Ex. 2
if 2 • n = 56
then
56 ÷ 2 = n
if 2 • 28 = 56
then
56 ÷ 2 = 28
n
25
=
4 20
"cross products"
division
n • 20 = 4 • 25
n • 20 = 100
5
20 100
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n=5
so:
5 25
=
4 20
-------------------------------------------------------------------------------------------------------PRACTICE: SOLVE FOR THE UNKNOWN IN EACH PROPORTION
1.
n
6
=
4 8
2.
n
9
=
7
21
4.
7
21
=
15
n
5.
32 1
=
n
3
3.
6.
6
24
=
n
36
n
25
=
12
4
----------------------------------------------------------------------------------------------------------
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PROPORTIONS
ANSWERS TO PRACTICE PROBLEMS
Page 4
1. 48 = 48 True
2. 75 = 27 False
3. 24 = 35 False
4. 240 = 240 True
5. 42 = 40 False
6. 36 = 36 True
Page 6
1. n = 3
2. n = 3
3. n = 9
4. n = 45
5. n = 96
6. n = 75