Unit 1.2, 1.3, and word problems

Alg. 2 (25-26)

Rational numbers

CAN be written as fractions

Decimal form stops or repeats (2.5 or 0.333)

Irrational numbers

CANNOT be written as fractions

Decimal form DOESN’T stops or repeat (7.4956)

Square roots of number that are not perfect squares (root 30)

What are integers, whole numbers, and natural numbers?

Rational numbers

Integers

Not a fraction

Includes negative numbers too

Whole numbers

Not a fraction

Starts from 0…and so on

Natural numbers

counting numbers

starts from 1…and so on

Symbol for Real Numbers

R

Symbol for Rational Numbers

Q

Symbol for Integers

Z

Symbol for Whole Numbers

W

Symbol for Natural Numbers

N

Symbol for Irrational Numbers

I

Irrational and Rational are both what type if numbers?

Real numbers

Commutative Property of Addition

a + b = b + a - order doesn’t matter

Commutative Property of Multiplication

a x b = b x a - order doesn’t matter

Associative Property of Addition

(a + b) + c = a + (b + c) - different grouping, same sum

Associative Property of Multiplication

(a x b) x c = a x (b x c) - different grouping, same product

Distributive Property

a (b+c) = ab + ac

Identity Property of Addition

a + 0 = a - doesn’t change anything

“0” is called the additive identity.

Identity Property of Multiplication

a x 1 = a - doesn’t change anything

“1” is called the multiplication identity

Inverse Property of Addition

a + (-a) = 0 - sum of both numbers is zero

Inverse Property of Multiplication

a (1/a) = 1 - product of both numbers is one

Closure Property:

If an operation is conducted on any two elements of the set, then the result of that operation is also within the set.

For example, the set of real numbers is closed under addition and multiplication

a + b = c

x*y = z

What’s a linear equation?

A linear equation in one variable is an equation that can be written in standard form as Ax + B = 0 where A and B are constants and A ≠ 0.

A number is a solution of a linear equation in one variable if ________ the number for the variable results in a true statement.

substituting

A linear equation can have ___ solution, ___ solution, or ______ solutions.

one, no, or infinite

Literal equations: When asked to solve for one variable in terms of the other variable(s), rewrite the equation such that the variable we are solving for is on _______ and does not appear on the other side

one side

For example, solve for y in terms of x. How will this be written:

y=..#x….