Math Rules Flashcards
What does the commutative property of addition state?
When you add two numbers you can reverse the order of the numbers without changing the sum.
What does the commutative property of multiplication state?
When you multiply two numbers, you can reverse the order of the numbers without changing the product.
What does the associative property of addition state?
when you have three numbers to add together, the final sum will be the same regardless of the way you group the numbers (two at a time) to perform the addition.
What does the associative property of multiplication state?
When you have three numbers to multiply together the final product will be the same regardless of the way you group the numbers (two at a time) to perform the multiplication.
What does the additive identity property state?
You have a real number, namely 0, whose sum with any real number is the number itself
What does the multiplicative identity property state?
You have a real number, namely 1, whose product with any real number is the number itself
What does the additive inverse property state?
Every real number has an additive inverse (its opposite) that is a real number whose sum with the number is 0.
Wha does the multiplicative inverse property state?
Every real number, except zero, has a multiplicative inverse ( its reciprocal) whose product number is 1
What does the distributive property state?
When you have a number times a sum (or a sum times a number), you can multiply each number separately first and then add the products
What does the zero factor property state?
If a real number is multiplied by 0, the product is 0; and if the product of the two numbers is 0, then at least one of the numbers is 0.
What is does zero exponent rule state?
x^0=1 if x is not equal to 0. (0^0 is undefined to has no meaning)
What does the unit fraction exponent rule state?
If x is a real number and n is a positive integer, then
x^1/n= x to the square root of n.
When n is even x is greater than or equal to 0
What does the rational exponent rule state?
If x is a real number and m and n are positive integers then
x^m/n= (x^1/n)^m or (x^m)^1/n
What does the product rule for the same base exponential expressions state?
x^mx^n= x^m+n
Add the exponents if the base is the same
What does the quotient rule for the same base expressions state?
xm/xn = x^m-n
If the base of the exponential expression is the same and you are dividing them, subtract the exponents.
What does the rule for a power to a power state?
(x^m)^p= x^mp
If you have to distribute an exponent, you have to multiply it
What does the rule for the power of a product state?
(xy)^p= x^py^p
Distribute the exponents to every term being multiplied in the parentheses
What does the rule for the power of a quotient state?
(x/y)^p = x^p/y^p
Distribute the exponent to every term that is in the fraction
How do you add and subtract polynomials?
Add or subtract the monomials with like terms.
How do you multiply monomials?
Multiply monomials by using the rule for exponents and the commutative and associative properties.
(Multiply the coefficients and the variables with exponents)
How do you multiply a polynomial by a monomial?
To multiply a polynomial by a monomial, multiply each term of the polynomial by the monomial.
How do you multiply binomials?
To multiply two binomials, multiply all the terms of the second binomial by the first binomial.
Use FOIL method
How do you multiply two polynomials?
To multiply two polynomials, multiple all the terms of the second polynomial by the first polynomial then combine like terms
How do you divide a polynomial by a monomial?
Divide each term of the polynomial by the monomial
How do you divide a polynomial by a polynomial?
Use long division
When do you use the factoring method of factoring out common factors?
If each term in the polynomial shares a common factor
When do you use the factoring method of the difference of squares?
If the expression represents a difference of squares
i.e. x^2-16 or 25x^2-9
When do you use the factoring method of using perfect square trinomials?
If the first and last terms are perfect squares and the middle term is twice the product of their square root.
When do you use the sum product pattern to factorize?
If the polynomial is of the form x^2+b^x+c and there are factors of c that add up to b.
When do you use the grouping method to factorize?
If the polynomial is of the form ax^2+b^x+c and there are factors of ac that add up to b
