8th Grade Algebra Review - Properties  

additive identity property - the sum of any number and 0 is equal to the number. 0 is the additive identity.

x + 0 = 0 + x = x

multiplicative identity property - the product of any number and 1 is equal to the number. 1 is the multiplicative identity.

8 · 1 = 8;  x · 1 = x

Multiplicative property of 0 - the product of any number and 0 is equal to 0.

8 · 0 = 0;  y · 0 = 0

multiplicative inverses or reciprocals - two numbers whose product is 1.

 7 · 1/7 = 1;  x · (1/x) = 1

closure property - a set of whole numbers is closed under an arithmetic operation if the results of the operation are all whole numbers.

The set of whole numbers is closed under addition since the sum of any two whole numbers is always a whole number. The set is also closed under subtraction and multiplication, but not under dividsion. ( 5 ÷ 8) does not result in a whole number.

distributive property -

8(6 + 4) = 8(6) + 8(4)

x(y - 7) = xy - 7x

40(3 1/4) = 40 (3 + 1/4) = 40(3) + 40 (1/4) = 120 + 10 = 130

commutative property -

s + t = t + s    (addition)

xy = yx    (multiplication)

associative property -

(m + n) + p = m + (n + p)     (addition)

(mn)p = m(np)    (multiplication)

substitution property -

if x =y, then x may be substituted for y