MTH121—Chapter 6
Fraction Operations and Properties
Fractions
: an ordered pair of whole numbers, such that
and
are whole numbers,
0
a
F
a
b
b
b
The term fraction can be used in two ways:
Numeral
indicates the number of parts to the whole;
Number
is the
relative amount of the whole.
Equivalency
is the merger of the two concepts,
a
an
b
bn
.
Cross Product
(test for equivalency):
iff
ac
ad
bc
bd
.
Cross Product
(test for order):
.
Density:
Between any two fractions is another fraction.
Techniques for finding fractions between fractions:
1.
Fraction Equivalency
7
3
21
11 3
33
22 23
,
33 33
8
3
24
11 3
33
2.
a
a c
c
b
b d
d
2
2 4
4
3
3 5
5
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View Full DocumentOperations with Fractions
:
Addition
:
Common Denominator:
a
c
a c
b
b
b
Measurement Models:
Region Model
Numberline Model
3 2
5
8 8
8
2
8
+
3
8
0
5
8
1
Unlike Denominator:
Cross Product Method:
a
c
ad bc
b
d
bd
3 7
4 5
3 4
21 20
41
5 7
5 7
35
Properties of Fraction Addition:
Closure:
the sum of fractions is a fraction
Commutativity:
a
c
c
a
b
d
d
b
Associativity:
a
c
e
a
c
e
b
d
f
b
d
f
Additive Identity:
00
aaa
b
b
b
b
b
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 Spring '11
 Staff
 Algebra, Addition, Fractions, Fraction, Elementary arithmetic, equal parts

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