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1 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 SLC Math Lab Lake Worth Basic Algebraic Operations 2 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 SLC Math Lab Lake Worth = 0 for a ≠ 0 = is undefined Basic Algebraic Operations