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## Ignore words

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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.
sum of a number and zero=the number
identity of multiplication
a x 1 = a
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.
x + (y+z) = y + (x + z) (changing grouping)
associative property of multiplication
When the grouping of factors changes, the products stays the same.
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.
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.
The sum of any number and 0 is the number.
Multiplicative identity property
The product of any number and 1 is the number.
The sum of 0 and any number is that number.
Zero Property
6 x 0 = 0
The additive identity is 0. a + 0 = 0 + a = a
Multiplicative Identity
A * 1 = A
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.
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