1 / 18

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.

marychughes
Download Presentation

PROPERTIES OF ALGEBRA

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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)

More Related