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Ch 2.5
Objective:
To multiply integers.
Properties
Commutative Property: a * b = b * a
Two numbers can be multiplied in either order
and the result is always the same.
For example: 4 * 6 = 6 * 4
Associative Property: (a * b) * c = a * (b * c)
Three numbers can be multiplied in any order
and the result will always be the same.
For example: (1 * 2) * 3 = 1 * (2 * 3)
More Properties
Identity Property: 1 * a = a
The product of 1 and a number will always be
the number.
For example: 1 * 11 = 11
Inverse Property: a * (1/a) = 1
The product of a number and its reciprocal
will always equal one.
For example: 10 * (1/10) = 1
Property & Definition
Zero Product Property: a * 0 = 0
The product of zero and any number will
always equal zero.
For example: 5 * _____ = 0
Reciprocal:
The reciprocal of a number is 1 divided by the
number.
For example: Reciprocal of a is 1/a.
Reciprocal of 1/a is a.
Rules for Multiplying Integers
Same Sign (+)
Evaluate 2 numbers at a time. If they have the
same sign, the result is always positive.
For example: 4 * 5 = 20
-4 (– 5) = 20
Opposite Signs (-)
Evaluate 2 numbers at a time. If they have
opposite signs, the result is always negative.
For example: 4 (–7) = -28
-4 (7) = -28
Odd # of Negatives = Negative
Even # of Negatives = Positive
Simplify.
1) 3  8  -24
5) 5  (8)  -40
2) 4  ( 9)  +36
6) 10 (4)  +40
3) 6  7  -42
7) 6 (4) (2) 
24 (-2) = -48
8) 5 (4) 2 
20 2 = +40
4) ( 2)( 5)( 3)  +30
Review
Simplify the following.
1) -6(7) = -42
5) (-9) -5 = -14
2) 6(-7) = -42
6) -9(-5) = +45
3) (6) -7 = -1
7) (+9) -5 = +4
4) (-6) -7 = -13
8) +9(-5) = -45
Simplify the following.
1) 34
4
2) (3)
3) 4 3
4) ( 4)
3
5) ( 2)
4
-81
6) (7  2) 2 25
+81
7) 7  22
-64
8) 6(3)2 54
3
-64
9) 6
16
10) 12 0 1
2
-36
Simplify the following.
1) 3(x)( x)
3x
6) 1(a)
2
2
2) 4(a)
5
4a
3) 6(k)
5
10
6k
10
a
2
7) x( x)(x)
8) 4(y)
5
x
3
4y
5
4
7
4) 5(m)
5m
7
5) (b)(b)(b)(b)
b
4
9) 3(t)
3t
4
10) 10( y)
2
10y
2