Math is proper

Commutative property

Order of operation does not affect the result.

Associative property

Order of grouping does not affect the result.

Distributive property

Multiply the outside term by ereach term inside the parentheses.

Identity properties

Adding inverse: opposite number cancel to 0. Multiplicative inverse: reiprocals multiply to 1.

Addition & subtraction property of equality

Whatever you add or subtract to one side, do the same to the other

Multiplication & division property of equality

Whatever you multiply or divide on one side, do the same to the other

Substitution property

once you find x, plug it in to find y.

Product rule

Same base? Add the exponents

Quotient rule

Same base dividing? Subtract the exponents

Power rule

Power raised to a power? Multiply the exponents.

Zero exponent rule

Anything to the power of 0 equals 1.

Negative exponent rule

A negative exponent means flip it to the denominator.

Fractional exponent rule

A fraction as an exponent means a root. Numerator = power, denominator = root.

Sum of two rationals

rational + rational = rational

Sum of rational + irrational

rational × rational = rational

Product of nonzero rational × irrational

nonzero rational × irrational = irrational

Transformation properties 1

f(x) + k → shift up/down

Transformation properties 2

f(x+k) → shift left/right

Transformation properties 3

kf(x) → stretch/compress vertically

Transformation properties 4

f(kx) → stretch/compress horizontally