Download Basic Algebraic Operations There are some basic properties in

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Basic Algebraic Operations
There are some basic properties in mathematics that apply to all real numbers;
when using variables in algebra these properties also apply.

Commutative Property of Addition
a+b=b+a
x+2=2+x
Subtraction is not commutative since 2 - 3 ≠ 3 -2; x -3 ≠ 3 - x

Associative Property of Multiplication
ab = ba
x·2 = 2·x
Notice that multiplication can be denoted by using different symbols;
by parenthesis “()”, the cross symbol “×”, by a point “·”, or by the absence
of a symbol:
(2)(3)
2×3
2·3
2a
In algebra, we avoid the use of “×” since we are dealing with variables
(letters), so “2a” denotes 2 times the variable a
Division is not commutative since
12 ÷ 6 ≠ 6 ÷ 12
Division is often shown in algebra by placing the dividend over the
divisor
𝑎
𝑏
which reads as “a divided by b”. This form is usually used when dealing
with fractions. The dividend is called the numerator and the divisor is
called the denominator.
The obelus ÷ is also used to denote division
a÷b
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Basic Algebraic Operations
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which also reads as “a divided by b.”

Additive Identity Property
a+0=a

Multiplicative Identity Property
a·1 = a

Additive Inverse Property
a–a=0

Multiplication Inverse Property
a·

1
𝑎
=1
Properties of Zero
a±0=a
a·0 = 0
0
𝑎
𝑎
0
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= 0 for a ≠ 0
= is undefined
Basic Algebraic Operations