8Th Grade Algebra - Property Of Real Numbers

Front 1

Commutative Property of Addition (Comm. +)

Back 1

For every number a,b; a+b=b+a. (Addition can be done in any order with the same result.)

Front 2

Commutative Property of Multiplication (Comm. X)

Back 2

For every number a,b; ab=ba. (Multiplication can be done in any order with the same result.)

Front 3

Associative Property of Addition (Assoc. +)

Back 3

For every number a,b, and c; a+(b+c)=(a+b)+c. (Addends can be grouped differently with the same result.)

Front 4

Associative Property of Multiplication (Assoc. X)

Back 4

For ever number a,c, and c; a(bc)=(ab)c. (Factors can be grouped differently with the same result.)

Front 5

Distributive Property of Multiplication over Addition (Dist. x/+)

Back 5

For ever number a,b, and c; a(b+c)=ab+ac. [Everything inside the ( ) must be multiplied by the number outside the ( ).]

Front 6

Identity Property of Addition (Ident. +)

Back 6

For every number a; a+0=a. (If you add zero to a number, the sum is identical to that number.)

Front 7

Identity Property of Multiplication (Ident. X)

Back 7

For ever number a; 1a=a. (If you multiply a number by 1, your product is identical to that number.)

Front 8

Inverse Property of Addition (Inv. +)

Back 8

For every number a; a+(-a)=0. (Any number added to its opposite equals zero.)

Front 9

Inverse Property of Multiplication (Inv. X)

Back 9

For ever number a; a · a = 1. (The product of 2 reciprocals is 1.)

Front 10

Multiplicative Property of Zero (Mult. Prop. 0)

Back 10

For every number a; a(0) = 0. (The product of any number and zero is zero.)

Front 11

Multiplicative Property of -1 (Mult. Prop. -1)

Back 11

For every number a; -1a = -a. (If you multiply a number by -1, it turns into an opposite.)

Front 12

Substitution Property of Equality (Subst. =)

Back 12

For every number a,b; if a=b then a can substitute for b. (If two quantities are equal, then they can replace each other.) Ex: 10+6+9=16+9

Front 13

Reflexive Property of Equality (Reflex. =)

Back 13

For every number a, a=a. (Every number equals itself.)

Front 14

Symmetric Property of Equality (Sym. =)

Back 14

For every a,b; If a=b then b=a. (If two quantities are equal, it doesn't matter which one goes on the left side of the equals sign.) Ex: 4.5=2.5+2, 2.5

Front 15

Transitive Property of Equality (Trans. =)

Back 15

For every number a,b,c; If a=b and b=c, then a=c. (If two quantities are both equal to a third quantity, then they are equal to each other.) 3=4-1 and 3=1+2, then 4-1=1+2

Front 16

Additive Property of Equality (Add. =)

Back 16

For every number a,b, and c; If a=b, then a+c=b+c. (Adding the same number to both sides of an equation keeps both sides of the equation equal.)

Front 17

Multiplicative Property of Equality (Mult. =)

Back 17

For every number a,b, and c; If a=b, then ac=bc. (Multiplying both sides of an equation by the same number keeps both sides equal.)