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Identity and Equality Properties 1-4

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Additive Identity The sum of any number and 0 is equal to the number. Symbols: a + 0 = a Example: 10 + n = 10 Solution: n = 0 10 + 0 = 10

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Multiplicative Identity The product of any number and 1 is equal to the number Symbol : a * 1 = a Example: 8 * n = 8 Solution: n = 1 because 8 * 1 = 8

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Multiplicative Property of 0 The product of any number and 0 is 0. Symbol: a * 0 = 0 Example: 8 * n = 0 Solution: The solution is 0 because 8 * 0 = 0

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Multiplicative Inverses or Reciprocals Two numbers whose product is 1 Symbol: a * b = 1 b a Example: 1 * n = 1 5 Solution: n = 5 Because: 1 * 5 = 1 1 5 1

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Properties of Equality Reflexive: any quantity is equal to itself. Symbols: a = a Example: 8 = 8 or 3 + 6 = 3 + 6 ( a number is equal to itself)

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Symmetric If one quantity equals a second quantity. Then the second quantity equals the first. Symbol: If a = b, then b = a Example: If 6 = 5 + 1, then 5 + 1 = 6

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Transitive I f one quantity equals a second quantity and the second quantity equals a third quantity, then the first quantity equals the third quantity. Symbol: If a = b and b = c, then a = c Example: If 5 + 4 = 6 + 3, and 6 + 3 = 9, then 5 + 4 = 9

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Substitution A quantity may be substituted for its equal in any expression Symbol: If a = b, then a may be replace by b in any expression Example: If n = 15, then 3n = 3*15 (substitute a number for a variable)

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Commutative Property The order in which you add or multiply does not matter Symbol : a + b = b + a Example: 5 * 3 = 3 * 5 Example 5 + 3 = 3 + 5

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Associative Property Grouping – Multiplication and Addition The way you group three or more numbers when adding or multiplying does not change their sum or product. Symbols: ( a + b) + c = a + (b + c) Example: ( 3 + 4) + 5 = 3 + (4 + 5) Example: (3 * 4) * 5 = 3 * (4 * 5) The order is the same – the grouping is different.

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Collecting Like Terms In order to add or subtract expressions with variables, the variables and exponents must be the same. You can add 3x + 6x because the variables are the same. Coefficients are numbers before the variables. Add the coefficients, keep the variables the same. 3x + 6x = 9x

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Like Terms You cannot add : 4x 2 + 9x. The variables are the same but the exponents are different. You can add: 4x 2 + 3x 2 because the variables and exponents are the same. 4x 2 + 3x 2 = 7x 2 Add the coefficients, the variables and exponents stay the same.

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Practice Underline the like terms in each problem. 13 m + 16mn + 4m + m 13m, 4m and m are like terms and can be added. They all have the same variable.

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Simplify 13 m + 16mn + 4m + m 18m + 16mn How did I get 18m?

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