# 2.1: Mathematical Fundamentals

Changing the order of addends does not change their sum
$A+B=B+A \\ 3+2=5 \;\; while, \;\; 2+3=5$

note, subtraction is not commutative

$A-B \neq B-A \\ 3-2=1\;\; while, \;\; 2-3=-1$

## Commutative Property of Multiplication

$AB=BA$

Note division not commutative
$\frac{A}{B} \neq\frac{B}{A} \\ \frac{3}{2}=1.5,\;\;while\;\;\frac{2}{3}=0.67$

$(A+B)+C=A+(B+C) \\(2+3)+4 =; 5+4=9\\and\\2+(3+4)=2+7=9$

## Associative Property of Multiplication.

$2(3x4)=(2x3)4 \\2(12)=24 \\and \\ 6(4)=24$

## Distributive Property of multiplication .

$A(B+C)=AB+AC \\ 2(3+4) =2(7)=14 \\ 2(3) +2(4) = 6+8=14$

note the reverse process allows you to factor out a value if you want to solve for it, so in the next equation, say you want to solve for T

$m_1c_1T+m_2C_2T=Q\\T(m_1c_1+m_2c_2)=Q$ and you can now solve for T

$T=\frac{Q}{m_1c_1+m_2c_2}$

## Exponentiation

Exponentiation is the repetition of multiplication

$2^n \text{ is 2 times 2 repeated n times } \\ 2^4=2(2)(2)(2)=16$

## Roots of a number

The root of a number to the power of n is the number that when multiplied n times equals the original number

$\sqrt[3]{64} =64^{ \frac{1}{3}} \text{ means what number when multiplied by itself 3 times equals 64}\\ \sqrt[3]{64} =4 \text{ because 4(4)(4) = 64}$