Chapter 1

Order of operations: PEMDAS

• Evaluate expressions inside grouping symbols (Parentheses).
• Evaluate all powers (Exponents).
• Multiply or divide from left to right (Multiply and Divide).
• Add or subtract from left to right (Add and Subtract).

Properties of equality

For all real numbers \(a, b, c\):

Property Name	Expression
Reflexive	\(a = a\)
Symmetric	If \(a = b\) then \(b = a\).
Transitive	If \(a = b\) and \(b = c\) then \(a = c\).
Substitution	If \(a = b\) then replace \(a\) with \(b\) in any expression.
Associative	\((a + b) + c = a + (b + c)\)
	\((a b) c = a (b c)\)
Commutative	\(a + b = b + a\)
	\(a b = b a\)
Distributive	\(a (b + c) = ab + ac\)
	\((b + c) a = ba + ca\)

Solving equations

• Apply order of operations.
• Apply properties of real numbers.

Feynman Technique for Problem-Solving

• Read the question.
• Think very hard.
• Write down the answer.