Properties of Numbers

Question 1

Reflexive property.

Answer 1

a number is always equal to itself

Example: 10 = 10

Question 2

Symmetric property.

Answer 2

For all real numbers x and y , if x=y , then y=x

For example, if 5 + 3 = 8, then 8 = 5 + 3

Question 3

Transitive property.

Answer 3

for all real numbers a = b and b = c, then a = c.

For example, if 5 + 3 = 8 and 8 = 4 × 2 then 5 + 3 = 4 × 2

Question 4

Commutative property of addition

Answer 4

Commutative property of addition. Changing the order of addends does not change the sum
For example, 2 + 3 = 3 + 2

Question 5

Commutative property of multiplication.

Answer 5

the order in which we multiply numbers does not change the product.
For example, 3 × 2 = 2 × 3

Question 6

Associative property of addition

Answer 6

Changing the grouping of addends does not change the sum

For example, (2 + 3) + 4 = 2 + (3 + 4)

Question 7

Associative property of multiplication

Answer 7

the way in which factors are grouped in a multiplication problem does not change the product.
For example, (2 × 3) × 4 = 2 × (3 × 4)

Question 8

Additive identity

Answer 8

we call 0 the additive identity because adding it preserves the identity of a number
For example, 3 + 0 = 3.

Question 9

Multiplicative identity

Answer 9

any number multiplied by 1, gives the same result as the number itself
For example, 4 × 1 = 4

Question 10

Additive inverse property

Answer 10

to change the positive number to a negative number and vice versa
For example, 2 + (–2) = 0

Question 11

Multiplicative inverse property.

Answer 11

a number times its multiplicative inverse equals 1

2 × 1/2 = 1

Question 12

Multiplicative property of zero

Answer 12

the product of any number and zero, is zero

For example, 3 × 0 = 0

Question 13

Zero-product property

Answer 13

that the product of two nonzero elements is nonzero

For example, if x(x + 2) = 0,then x = 0 or x + 2 = 0.