epdf.pub_cbest-cliffs-test-prep13a9b242c7cb4125e6cca92d00a73d5a41681

Part IV: Mathematics Review
Some Properties (Axioms) of Multiplication
■
Commutative means that the order does not make any difference.
2# 3=
3#
2
a# b=
b#
a
Note: Commutative does not hold for division.
■
2'
4!
4'
2
Associative means that the grouping does not make any difference.
^2# 3h# 4=
2# ^3#
4h
^a# bh# c=
a# ^b#
ch
The grouping has changed (the parentheses moved), but the sides are still
equal.
Note: Associative does not hold for division.
^8' 4h' 2!
8' ^4'
2h
■ The identity element for multiplication is 1. Multiplying any number by 1
gives the original number.
■
3# 1=
3
a# 1 = a
The multiplicative inverse is the reciprocal of the number. Any number
multiplied by its reciprocal equals 1.
2 × 1 ⁄2 = 1; therefore 2 and 1 ⁄2 are inverses
a × 1 ⁄a = 1; therefore a and 1 ⁄a are inverses
A Property of Two Operations
■
The distributive property is the process of distributing the number on the
outside of the parentheses to each number on the inside.
23 ^ + 4h= 23 ^ h+
24 ^ h
a^b+ ch= a^bh+
a^ch
Note: You cannot use the distributive property with only one operation.
3 (4 × 5 × 6) ≠ 3(4) × 3(5) × 3(6)
a^bcdh!
a^bh# a^ch#
a^dh or a^bcd h!
^abh^ach^adh
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