Chapter 5 Math Study Guide

Absolute Value

b/a

What is the formula for finding absolute value

a/b

Decimal to scientific?

Right neg left pos

Scientific to decimal?

Right pos left neg

Integer

Pos neg zero

Natural

Whole positive numbers

Rational

Fraction/decimal

Irrational

Pi radical

Real number

Everyone

Communative

Change order

Associative

Change group

Identity

Stays the same

Inverse

Cancels out

Absolute value is always what

Positive

How many times you move a number around not the actual addition

Clock addition

Everyone multiplies

LCM

Friends (common) only multiply

GCD

What too thing do you multiply common numbers to find

LCM and GCD

Multiplying with the BIGGEST exponent

LCM

Multiplying with the SMALLEST exponent

GCD

How do you find prime factorization

Factor tree and multiply ALL factors

How do you multiply fractions with different bottoms

Does not matter multiply across

Do the equations make sense for what is being asked?

Closure

When you are simplifying a negative exponent (like 2^-7) what do you do with the negative?

Leave it alone and throw it on the end answer

When you are trying to use PEMDAS and there are multiple multiplications/divisions how do you tackle that?

Work on it left to right

How do you multiply a radical with a whole number

Put the whole number in front of the radical and simplify

If you are adding/subtracting radicals what can you do?

Put them under one big radical

How do you simplify a radical?

1.Factor tree

2.Are there perfect squares (if not then its already simplified)

3.Multiply all the left side numbers together that make a perfect square

4.Put that number and the final prime number (last right number) underneath a radical

5. See if you can take any perfect squares out

When you are rationalizing an equation what happens when you multiply a radical with a radical

the radical cancels out

How do you solve radical equatations with the same base

Ignore the base and work on whats left

How do you solve radical equations with different bases?

1. Break each radical into 2 factors (one perfect square and one prime)

2. Take out perfect square

3. Multiply it by whatever is in front of the radical

4. Solve with the same base (ignore the bases)

What do radicals only like

Same bases

If there is nothing in front of a radical what is it secretly

1

When you are simpfying a fraction with a radical on top and bottom what do you need to do

Rationalize the denominator (get rid of the radical)