Question

Choose two axioms that allow 6 + (x + 5) to be written x + 11.

A) commutative - addition
B) distributive
C) associative - multiplication
D) symmetric
E) commutative - multiplication
F) associative - addition
G) identity - addition

Answer 1

Basic number properties:

• The Distributive Property:
  `a\cdot (b+c)=a\cdot b+a\cdot c;`
• The Associative Property for addition:
  `a+(b+c)=(a+b)+c;`
• The Associative Property for multiplication:
  `a\cdot (b\cdot c)=(a\cdot b)\cdot c;`
• The Commutative Property for addition:
  `a+b=b+a;`
• The Commutative Property for multiplication:
  `a\cdot b=b\cdot a;`
• Identity Property : Any number add to the zero the answer is the number itself;
• The symmetric property states that if one number is equal to a second number, then the second number is equal to the first number.

For the expression 6 + (x + 5):

1. use The Commutative Property for addition - 6+(x+5)=(x+5)+6;
2. use The Associative Property for addition - (x+5)+6=x+(5+6)=x+11.

Answer 2

associative means that you can move the parenthesis around the problem and still get the same answer. like (4+2)+3=4+(2+3)
first & sixth are the true