Quizlet Property List for Algebra Honors 8

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  1. addition property of equality: Adding the same quantity to both sides of an equation. (If a=b, then a+c=b+c)
  2. additive inverse: Adding the opposite the equal zero, and used to praove an opposite. (a+-a=0, a-a=0, and used to prove that if a is real, negative a is real)
  3. associative of addition: in an equation using additon and subtraction, the order will remain the same but parenthesis groupings will change. [(1+2)+3=1=(2+3)]
  4. associative of multiplication: in an equation using multiplication and division, the order will remain the same but parenthesis groupings will change. [2(3)4=(2)3(4)]
  5. axiom of closure: If (ab) is real, then a+b is real. ( if 3+4=7 s real, 3(4)=12 is real)
  6. cancellation: To multiply a negative by a negative. [-(-a)=a]
  7. commutative of addition: To change the order of an equation that uses addition or subtraction. (3+4=4+3)
  8. commutative of multiplication: Changes the order of an eqation that uses multiplication and or division. [(3)4=(4)3]
  9. definition of division: Rules for dividing fractions. [3/4=(3/4)/1=3(1/4)=3/4]
  10. definition of subtraction: Just like switch-switch! [a+(-b)=a-b] Just Asking; doesn't switch switch go along with yellow-yellow?
  11. distributive: To multiply a value through parenthesis. Only works if only additon and subtraction are in the parenthesis. [a(b+c)=ab+ac
  12. division property of equality: Dividing the same quantity to both sides of an equation. (If a=b, then a/c=b/c)
  13. hypothesis: To prove that any variable is real. (a, b, and c are real numbers.)
  14. identity of addition: To add zero. (a+0=a)
  15. identity of multiplication: To multiply by 1. [a(1)=a]
  16. multiplication property of equality: Multiplying the same quantity to both sides of an equation. (If a=b, then ac=bc)
  17. multiplicative inverse: To multiply by the reciprocal, and used to prove recirocals are real. [a(1/a)=1, and to prove that if a is real, then 1/a is real)
  18. multiplicative property of negative one: To multiply by negative one. [-1(a)=-a]
  19. multiplicative property of zero: To multiply by zero. [a(0)=0]
  20. opposites in products: The rules of multiplying by integers. [-a(b)=-ab, a(b)=ab, and -a(-b)=ab]
  21. opposites of a sum: Like the distributive property, but used when only distributing a negative through. [-(a+3)=-a-3]
  22. reciprocal of a product: Seperating one fraction into two. [1/ab=1/a(1/b)]
  23. reflexive: Looks exactily the same on both sides. (a=a)
  24. substitution: To replace a value or actually complete the given operations. ( if a=3, and a=b, then 3=b)
  25. subtraction property of equality: Subtracting the same quantity to both sides of an equation. (If a=b, then a-c=b-c)
  26. symmetric: You can flip both sides of an equal side to still have a true eqation. (3=a, then a=3)
  27. transitive: Usually used at the end of a proof. To sum up. (if a=b, and b=c, then a=c)