Properties

Question 1

Commutative Property

Answer 1

order of the values does not matter;
a + b=b+a, 2+3=3+2;
y · x = x · y; 5 · 4= 4 · 5

Question 2

Associative Property

Answer 2

grouping of values doesn’t matter:
(a+b) + c= a + (b+c); (5+1) + 3= 5 + (1+3)
(a x b) x c= a x (b x c);(2 x 4) x 7= 2 x (4 x 7)

Question 3

Identity Property

Answer 3

stays the same;
a+0=0
a x 1= 1

Question 4

Inverse Property

Answer 4

Using the opposite to “cancel” a value;
a + (-a)=0;
a x 1/a=1

Question 5

Property of Zero

Answer 5

Multiplying by 0 always equals 0;

a x 0=0

Question 6

Distributive Property

Answer 6

Multiply a value to and expression inside (. );
a (b + c ) = ab + ac
2 (x+7)= 2x+14
-5(x-z)= -5y + 5z

Question 7

Reflexive Property

Answer 7

A value always equals itself;
16=16
5x=5x

Question 8

Symmetric Property

Answer 8

If a = b, then b = a;

If x=3 then 3=x

Question 9

Transitive Property

Answer 9

If a =b, and b=c, then a=c;

If 4+3=7 and 7 =√49, then 4+3 = √49

Question 10

Closed Set

Answer 10

When you use an operation, the numbers of that set will produce a number within the set.

Question 11

Open (Not closed set)

Answer 11

When you use an operation within a set, and it doesn’t produce a number with in the set.

Question 12

Integers are closed under multiplication.

Answer 12

True

Question 13

Odd numbers are closed under addition.

Answer 13

False. 3+7=10