Math Rules

Question 1

What does the commutative property of addition state?

Answer 1

When you add two numbers you can reverse the order of the numbers without changing the sum.

Question 2

What does the commutative property of multiplication state?

Answer 2

When you multiply two numbers, you can reverse the order of the numbers without changing the product.

Question 3

What does the associative property of addition state?

Answer 3

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.

Question 4

What does the associative property of multiplication state?

Answer 4

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.

Question 5

What does the additive identity property state?

Answer 5

You have a real number, namely 0, whose sum with any real number is the number itself

Question 6

What does the multiplicative identity property state?

Answer 6

You have a real number, namely 1, whose product with any real number is the number itself

Question 7

What does the additive inverse property state?

Answer 7

Every real number has an additive inverse (its opposite) that is a real number whose sum with the number is 0.

Question 8

Wha does the multiplicative inverse property state?

Answer 8

Every real number, except zero, has a multiplicative inverse ( its reciprocal) whose product number is 1

Question 9

What does the distributive property state?

Answer 9

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

Question 10

What does the zero factor property state?

Answer 10

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.

Question 11

What is does zero exponent rule state?

Answer 11

x^0=1 if x is not equal to 0. (0^0 is undefined to has no meaning)

Question 12

What does the unit fraction exponent rule state?

Answer 12

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

Question 13

What does the rational exponent rule state?

Answer 13

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

Question 14

What does the product rule for the same base exponential expressions state?

Answer 14

x^mx^n= x^m+n
Add the exponents if the base is the same

Question 15

What does the quotient rule for the same base expressions state?

Answer 15

xm/xn = x^m-n
If the base of the exponential expression is the same and you are dividing them, subtract the exponents.

Question 16

What does the rule for a power to a power state?

Answer 16

(x^m)^p= x^mp
If you have to distribute an exponent, you have to multiply it

Question 17

What does the rule for the power of a product state?

Answer 17

(xy)^p= x^py^p
Distribute the exponents to every term being multiplied in the parentheses

Question 18

What does the rule for the power of a quotient state?

Answer 18

(x/y)^p = x^p/y^p
Distribute the exponent to every term that is in the fraction

Question 19

How do you add and subtract polynomials?

Answer 19

Add or subtract the monomials with like terms.

Question 20

How do you multiply monomials?

Answer 20

Multiply monomials by using the rule for exponents and the commutative and associative properties.

(Multiply the coefficients and the variables with exponents)

Question 21

How do you multiply a polynomial by a monomial?

Answer 21

To multiply a polynomial by a monomial, multiply each term of the polynomial by the monomial.

Question 22

How do you multiply binomials?

Answer 22

To multiply two binomials, multiply all the terms of the second binomial by the first binomial.
Use FOIL method

Question 23

How do you multiply two polynomials?

Answer 23

To multiply two polynomials, multiple all the terms of the second polynomial by the first polynomial then combine like terms

Question 24

How do you divide a polynomial by a monomial?

Answer 24

Divide each term of the polynomial by the monomial

Question 25

How do you divide a polynomial by a polynomial?

Answer 25

Use long division

Question 26

When do you use the factoring method of factoring out common factors?

Answer 26

If each term in the polynomial shares a common factor

Question 27

When do you use the factoring method of the difference of squares?

Answer 27

If the expression represents a difference of squares

i.e. x^2-16 or 25x^2-9

Question 28

When do you use the factoring method of using perfect square trinomials?

Answer 28

If the first and last terms are perfect squares and the middle term is twice the product of their square root.

Question 29

When do you use the sum product pattern to factorize?

Answer 29

If the polynomial is of the form x^2+b^x+c and there are factors of c that add up to b.

Question 30

When do you use the grouping method to factorize?

Answer 30

If the polynomial is of the form ax^2+b^x+c and there are factors of ac that add up to b