Properties of Real Numbers - 7th grade

Question 1

Identity property of addition

Answer 1

a + 0 = a and 0 + a = a

Question 2

Identity property of multiplication

Answer 2

a x 1 = a and 1 x a = a

Question 3

Commutative property of addition

Answer 3

a + b = b + a

Question 4

Commutative property of multiplication

Answer 4

a x b = b x a

Question 5

Associative property of addition

Answer 5

(a+b)+c = a+(b+c)

Question 6

Associative property of multiplication

Answer 6

(axb)c = a(bxc)

Question 7

Inverse property of addition

Answer 7

a + (-a) = 0

-a + a = 0

Question 8

Inverse property of multiplication

Answer 8

a x 1/a = 1

1/a x a = 1(a~0)

Question 9

Distributive properties

Answer 9

a(b+c) = ab + ac
a(b-c) = ab - ac
(b+c)a = ba + ca
(b-c)a = ba - ca

Question 10

Property of equality for addition

Answer 10

a = b, then a + c = b + c

Question 11

Property of equality for subtraction

Answer 11

a = b, then a - c = b - c

Question 12

Property of equality for multiplication

Answer 12

a = b, then a x c = b x c

Question 13

Property of equality for division

Answer 13

a = b, and c~0, then a / c = b / c

Question 14

Property of equality for substitution

Answer 14

a = b, then ‘b’ can replace ‘a’ in any expression

Question 15

Property of equality for reflexive

Answer 15

a = a

Question 16

Property of equality for symmetric

Answer 16

a = b, b = a

Question 17

Property of equality for transistive

Answer 17

a = b, b = c, a = c

Question 18

Zero-Product Property

Answer 18

ab = 0, a = 0 or b = a

Question 19

Cross product property

Answer 19

a / b = c / d is equivalent to ad = bc

Question 20

Property of inequality for addition

Answer 20

a > b, then a + c > b + c

Question 21

Property of inequality for subtraction

Answer 21

a > b, then a - c > b - c

Question 22

Property of inequality for multiplication

Answer 22

a > b and c > 0, then ac > bc

Question 23

Property of inequality for division

Answer 23

a > b and c > 0, then a/c > b/c

Question 24

Transitive

Answer 24

a > b and b > c, then a > c

Question 25

Comparison

Answer 25

a = b + c and c > 0, then a > b

Question 26

Properties of the Zero Exponent

Answer 26

a^0 = 1

Question 27

Properties of the Negative Exponent

Answer 27

a^ - n = 1 / a^n

Question 28

Properties of the product of powers

Answer 28

a^m x a^n = a^m + n

Question 29

Properties of the quotient of powers

Answer 29

a^m / a^n = a^m - n

Question 30

Properties of the power of a power

Answer 30

(a^m)^n = a^m * n