Complex number system

Expressions

An algebraic expression is a mathematical phrase made up of one or more numbers or variables

3x^2 - 2xy+6

2(x + 8y)

distributive property

distributive property is when you have a number outside of a parentesis and you have to distribute the outside number to the inside numbers

What are variables?

variables are place holders for numbers

Equations

1 and 2 steps equations

One and two step equations are different because the simplification process is already finished for you. When you have and 1 step equation and when you start a 2 step equation you have to simplify for yourself.

Equations have expressions being compared with a equal sign and have to be equal

2+4=6

3+9=12

In order to know if a equation is correct you have to solve for a variables

3x+3=5y-1

x=2 y=2

3(2)+3=5(2)-1
6+3=10-1
9=9

This method is called substitution where you input the numbers in for the variables.

Inequalities

Inequalities are when both side of the equal sides are not equal they are also used to tell if expressions are equal or not.

12+6=17

27-5=12

In order to know that a inequality is not equal you have to simplify it fully

Square roots

Cube roots

4^3=64

cube root of 64=4

Cube roots are only used whenever a number and can have a exponent of 3 can fit inside the original number 3 times.

Cube roots also use the radical sign but they put a 3 on top of the left side of the radical sign

What is a radical sign that is over a number?

The radical sign tells you to figure out the base of the original exponent and and then multiply the base by itself once

Without a number outside to the radical sign you can just assume that it is just a square roots

Square roots are the inverse operation of exponents

4^2=16

square root of 16=4

Exponents

Exponent Rules

Negative exponent rule

B^-N=1/B^N

When you multioly the base by a negative exponent you flip it to make it a fraction and flip the negative exponent and make it positive

Zero exponent rule

B^0=1

When you multiply the base by 0 you get 1 because anytime you multiply any number by 0 you get 1.

product of exponent rule

A^mxn=a^m+n

This means whenever you multiply a exponent you multiply the variables together

Quotient of exponent rule

A^m/n=A^m-n

When you divide exponents you subtract the variables from each other to determine how many times you multiply the base by itself

Power to Power rule

B^n)B^m=B^mxn

This means that whenever you multiply a exponent by a exponent with the same base then you make them come together

One exponent rule

B^1=B

When you multiply a positive 1 you keep the base because whenever you multiply any number by 1 you keep the number

These rules are used to find out how many times to multiply a number by itself.

What are Exponents?

Exponents are the small numbers above another number. They are used to tell you how many times you have to multiply the number by itself

Number families

Whole number family

(1,2,3,4,5,6)

Any positive whole number

Natural number family

(0,1,2,3,4,5,6)

Any positive whole number including zero.

Integer number family

(-3-2-1,0,1,2,3)

Any positive or negative whole number including zero

Irrational number family

(3.179580729_,pi,5.1327957324_)

Any repeatng without a pattern or non-terminating numbers

Why do algebraic expressions need variables?

They need variables because the algebraic expression would not be algebraic if they did not have variables

What is simplification?

Simplification is when you break topics down for other people to understand.

Relationships between expression and equation

expressions are used to write numbers using a sequence of symbols and equations are used to show the equality of numbers

Expression 2(x + 8y)
Equation 2(x + 8y) = 3x + 4

Rational number family

(1.75,0.22_,3.22,4.82,1.33_)

Blue=Explanations

Orange=Topics

Yellow=Questions

Tan=Answers

Purple=Examples

Red=MAIN TOPIC

Scientific notation

Way of writing really small or large numbers

1x10^3=1000

1x10^-3=0.001

Base is always 10

coefficient = 1-9

If the exponent is negative then the number decreases and if it is positive then It increases

Prime factorization

Prime factorization is used to write numbers using prime numbers

__24__
_4_x_6_
2x2|2x3