Properties of Real Numbers - 7th grade Flashcards
Identity property of addition
a + 0 = a and 0 + a = a
Identity property of multiplication
a x 1 = a and 1 x a = a
Commutative property of addition
a + b = b + a
Commutative property of multiplication
a x b = b x a
Associative property of addition
(a+b)+c = a+(b+c)
Associative property of multiplication
(axb)c = a(bxc)
Inverse property of addition
a + (-a) = 0
-a + a = 0
Inverse property of multiplication
a x 1/a = 1
1/a x a = 1(a~0)
Distributive properties
a(b+c) = ab + ac a(b-c) = ab - ac (b+c)a = ba + ca (b-c)a = ba - ca
Property of equality for addition
a = b, then a + c = b + c
Property of equality for subtraction
a = b, then a - c = b - c
Property of equality for multiplication
a = b, then a x c = b x c
Property of equality for division
a = b, and c~0, then a / c = b / c
Property of equality for substitution
a = b, then ‘b’ can replace ‘a’ in any expression
Property of equality for reflexive
a = a
Property of equality for symmetric
a = b, b = a
Property of equality for transistive
a = b, b = c, a = c
Zero-Product Property
ab = 0, a = 0 or b = a
Cross product property
a / b = c / d is equivalent to ad = bc
Property of inequality for addition
a > b, then a + c > b + c
Property of inequality for subtraction
a > b, then a - c > b - c
Property of inequality for multiplication
a > b and c > 0, then ac > bc
Property of inequality for division
a > b and c > 0, then a/c > b/c
Transitive
a > b and b > c, then a > c
Comparison
a = b + c and c > 0, then a > b
Properties of the Zero Exponent
a^0 = 1
Properties of the Negative Exponent
a^ - n = 1 / a^n
Properties of the product of powers
a^m x a^n = a^m + n
Properties of the quotient of powers
a^m / a^n = a^m - n
Properties of the power of a power
(a^m)^n = a^m * n
