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PROPERTIES OF ALGEBRA

PROPERTIES OF ALGEBRA. Additive Identity. Multiplicative Identity. a · 1 = a Note: the value remains the same Example: 7 · 1 = 7. Additive Inverse. a + (-a) = 0 Note: the terms cancel each other out and equal the identity. Example: 2 + (-2) = 0. Multiplicative Inverse.

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PROPERTIES OF ALGEBRA

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  1. PROPERTIES OF ALGEBRA

  2. Additive Identity

  3. Multiplicative Identity • a · 1 = a • Note: the value remains the same • Example: 7 · 1 = 7

  4. Additive Inverse • a + (-a) = 0 • Note: the terms cancel each other out and equal the identity. • Example: 2 + (-2) = 0

  5. Multiplicative Inverse

  6. Property of Zero (Multiplication) • a · 0 = 0 • Note: any term multiplied by 0 is equal to 0 • Example: 5 · 0 = 0

  7. Commutative Property

  8. Associative Property

  9. Reflexive Property of Equality • a = a • Note: the term is equal to itself • Example: 5x + 1 = 5x + 1

  10. Symmetric Property of Equality • If a = b, then b = a • Note: there are two equations and the left and right sides are switched • Example: if x + 3 = 7, then 7 = x + 3

  11. Transitive Property of Equality • If a = b and b = c, then a = c • Note: there are three equations that follow a pattern • Example: if x = 3 + 5 and 3 + 5 = 8, then x = 8

  12. Substitution Property of Equality • If a = b then “a” can replace “b” • Note: substitution means replacement • Example: if x = 2, then 5x + 3 = 5(2) + 3

  13. Distributive • a (b + c) = ab + ac • Note: a coefficient is multiplied by at least two terms. • Example: 2 (x + 5) = 2x + 10

  14. Addition Property of Equality • If a = b, then a + c = b + c • Note: the same thing is added to both sides of the equation • Example: if x – 10 = 15, then x = 25(added 10 to each side)

  15. Subtraction Property of Equality • If a = b, then a – c = b – c • Note: the same thing is subtracted to both sides of the equation • Example: if y + 5 = 70, then y = 65(5 is subtracted from both sides)

  16. Multiplication Property of Equality • If a = b, then a · c = b · c • Note: the same thing is multiplied to both sides of the equation • Example: If ½ x = 10, then x = 20(each side is multiplied by 2)

  17. Division Property of Equality • If a = b, then a/c = b/c • Note: the same thing is divided to both sides of the equation • Example: If 5x = 20, then x = 4(each side is divided by 5)

  18. Closure Property • If a & b are integers, then a+b is an integer. • If you perform an operation on any two numbers of a set, the solution is still in the set. • 5 * 2 = 10 is closed for integers (5, 2 and 10 are all integers) • Division is NOT closed for integers because (5 ÷ 2 = 2.5, and 2.5 is NOT an integer)

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