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distributive property

Multiplying a sum by a number is the same as multiplying each term by the number and then adding (or subtracting ) the products.

5(x+7)=5x+35

Distributive Property

8(0)=0

Multiplicative Property of Zero

48∙f=0

Multiplicative Property of Zero

y∙9=0

Multiplicative Property of Zero

Commutative

Changing the order of the factors does not change the product.

associative

Changing the grouping of the factors does not change the product.

Distributive

This is done by breaking a large fact into two smaller known facts.

identity of addition

sum of a number and zero=the number

identity of multiplication

a x 1 = a

commutative property of addition

If the order of the terms changes, the sum stays the same.

commutative property of multiplication

If the order of factors changes, the product stays the same.

Associative Property of Additon

x + (y+z) = y + (x + z) (changing grouping)

associative property of multiplication

When the grouping of factors changes, the products stays the same.

Identity Property of Addtion

k + 0 = k (The sum of any # and zero is the original #)

identity property of multiplication

The product of 1 and any number is that number.

Zero Property of Mulitiplication

Any number multiplied by zero equals zero.

Inverse Property of Multiplication

The product of a nonzero number and its multiplicative inverse, or reciprocal, is 1.

Multiplicative property of -1

Multiplying a number by -1 equals its opposite.

Inverse Property of Addition

8 + (-8) = 0

Associative Property

(1 + 2) + 3 = 1 + (2 + 3)

Commutative Property

3 + 2 = 2 + 3

zero property of multiplication

The product of any number and zero is zero.

Additive identity property

The sum of any number and 0 is the number.

Multiplicative identity property

The product of any number and 1 is the number.

Identity Property of Addition

The sum of 0 and any number is that number.

Zero Property

6 x 0 = 0

Additive Identity

The additive identity is 0. a + 0 = 0 + a = a

Multiplicative Identity

A * 1 = A

additive inverse

the opposite of a number

multiplicative inverse

reciprocal of a number

Multiplicative Property of Zero

A number times 0 = 0

Distibutive

Take a number of the outside of the parenthesis and multiply it on the inside.

Addition Property of Equality

For all real numbers x, y, and z, if x = y, then x + z = y + z.

Subtraction Property of Equality

For all real numbers x, y, and z, if x = y, then x - z = y - z.

Multiplication Property of Equality

For all real numbers x, y, and z, if x = y, then xz = yz.

Division Property of Equality

For all real numbers x, y, and z, if x = y, and z ≠ 0, then x/z = y/z. You can divide each side of an equation by the same non-zero number and not change its truth value.

Substitution

The replacement of letters/variables in an algebraic expression.

Reflective

The exact same thing on each side of the equal sign

Symmetric

Flip the left side of the equation to the right side.

Trabsitive

Three Parts: part 1= part 2