How to Find a Common Denominator
What? Common denominators exist when the denominator of each fraction is the same.
When? Common denominators are needed when:
(1) Comparing fractions,
(2) Adding fractions,
(3) Subtracting fractions.
Why? The old adage that “You cannot compare apples and oranges,” is true for common
denominators. In order to add, subtract, or compare fractions, first find a common
denominator.
How?
(1)
(2)
(3)
There are several ways to derive a common denominator, but the easiest way may be:
Multiply the denominators to secure a number into which all the denominators divide.
Determine what number was multiplied to find each new denominator.
Multiply the numerator by that same number to create an equivalent fraction.
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and
3
Example: To find a common denominator between
3
.
4
(1) Multiply 3 × 4 = 12.
(2) Multiply the first fraction by 4 and the second fraction by 3.
(3)
1 4
∙ = 4 and 3 ∙ 3 = 9 ∴ 1 = 4 and 3 = 9 .
3 4 12
4 3 12
4 12
3 12
Example: To find a common denominator between 3 and 2 .
7
5
(1) Multiply 7 × 5 = 35.
(2) Multiply the first fraction by 5 and the second fraction by 7.
3 5 15
∙
=
and 2 ∙ 7 = 14 ∴ 3 = 15 and 2 = 14 .
7 5
5 7 35
7 35
5 35
35
Example: To compare fractions…which is greater 5 or 1 ?
8
2
1
(1) Change
to 8ths by multiplying both numerator and denominator by 4.
2
(2) 1 = 4
2 8
(3) 5 > 4 meaning 5 is greater than 4 .
8
8
8
8
How to Find the Mean or Average
(1) Add the quantities.
(2) Divide the sum (∑) by the number of quantities being added.
(3) The answer is the mean or average, symbol used: X .
Formula for Finding an Average:
X=
X 1 , + , X n
N
Example: Find the mean or average of the following: 3.15, 4.6, 12, 9.45.
(1) Add the quantities ∑= 29.20.
(2) Divide the sum by the number of entries.
(3) X = 7.30.
How to Write Algebraic Expressions
(1) Read the problem carefully.
(2) Whenever there is an unknown quantity, designate the unknown with some lower
case letter; variables are always written in lower case.
(3) If there are two related unknown quantities, it is generally helpful to let the variable
stand for the smallest unknown.
(4) Place the numbers or variables in juxtaposition to indicate multiplication.
(5) Place the numbers or variables in fraction form to indicate division.
Examples:
a) Three times a number decreased by 8 ↔ 3n – 8.
b) A number increased by 12 ↔ b + 12.
c) The product of a number and 9 ↔ 9a.
d) A number divided by 3 ↔ n .
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e) Four times a number divided by 3 increased by 5 ↔ 4( n ) + 5.
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