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# Linear Algebra Ch.2

### Simplifying with Variables

TermDefinition
Additive Identity The number 0 is called this because adding 0 to any number does not change the number. For example, 7 + 0 = 7.
Additive Inverse The number you need to add to a given number to get a sum of 0. For example, the additive inverse of −3 is 3. It is also called the opposite.
Associative Property of Addition When adding three or more numbers or terms together, grouping is not important. That is:(a + b) + c = a + (b + c) For example, (5 + 2) + 6 = 5 + (2 + 6)
combining like terms Combining two or more like terms simplifies an expression by summing constants and summing those variable terms in which the same variables are raised to the same power. For example, 3x + 7 + 5x − 3 gives 8x + 4
Commutative Property of Addition When adding two or more numbers or terms together, order is not important. That is: a + b = b + a For example, 2 + 7 = 7 + 2
Equation Mat Puts two Expression Mats side-by-side to find the value(s) which make the expressions equal. Legal moves are used to find the value(s) that makes the expressions equal.
evaluate To find the numerical value of. To do this to an expression, substitute the value(s) given for the variable(s) and perform the operations according to the order of operations. For example, evaluating 2x + y − 10 when x = 4 and y = 3 gives the value 1.
Expression Comparison Mat Puts two Expression Mats side-by-side so they can be compared to see which represents the greater value.
Multiplicative Identity Multiplying any number by 1 does not change the number. For example, 7(1) = 7.
Multiplicative Inverse The number we can multiply by to get the multiplicative identity, For example, for the number 5, and the number 1/5
non-commensurate If no whole number multiple of one measurement can ever equal a whole number multiple of the other.
Order of Operations The specific order in which certain operations are to be carried out to evaluate or simplify expressions: parentheses/grouping symbols, exponents (powers or roots), multiplication/division (left to right), and addition/subtraction (left to right).
term A single number, variable, or the product of numbers and variables. In an expression, these are separated by addition or subtraction signs.
variable A symbol used to represent one or more numbers.
Associative Property of Multiplication When multiplying three or more numbers or terms together, grouping is not important. That is:(a · b) · c = a · (b · c) For example, (5 · 2) · 6 = 5 · (2 · 6)
Identity Property of Addition Adding zero to any expression gives the same expression. That is: a + 0 = a For example, 6 + 0 = 6
Identity Property of Multiplication Multiplying any expression by one gives the same expression. That is: 1 · a = a For example, 1 · 6 = 6
Commutative Property of Multiplication When multiplying two or more numbers or terms together, order is not important. That is: a · b = b · a For example 3 · 5 = 5 · 3
Created by: EMarshall8