The 5 Basic Rules of Algebra
1. Commutative Rule
Addition: a + b = b + a
Multiplication: a × b = b × a
2. Associative Rule
Addition: (a + b) + c = a + (b + c)
Multiplication: (a × b) × c = a × (b × c)
3. Distributive Rule
a × (b + c) = (a × b) + (a × c)
4. Identity Rule
Addition: a + 0 = a
Multiplication: a × 1 = a
5. Inverse Rule
Addition: a + (-a) = 0
Multiplication: a × (1/a) = 1
Golden Rules of Mathematics
1. Order of Operations (PEMDAS/BODMAS)
- Brackets/Parentheses
- Orders (Exponents/Powers)
- Multiplication and Division (left to right)
- Addition and Subtraction (left to right)
2. The Equals Rule
Things equal to the same thing are equal to each other
3. Properties of Zero
- Any number plus zero equals the number
- Any number times zero equals zero
4. Properties of One
- Any number times one equals the number
- Any number divided by one equals the number
5. Sign Rules
- Positive × Positive = Positive
- Negative × Negative = Positive
- Positive × Negative = Negative
General Rules in Math
Consistency Rule
Mathematical statements must be consistent across all operations
Substitution Rule
Equal values can be substituted for each other in any expression
Addition Rule
- When adding positive numbers, the sum increases
- When adding negative numbers, the sum decreases
Multiplication Rule
- Positive × Positive = Positive
- Negative × Negative = Positive
- Positive × Negative = Negative
The Standard Rule in Math
The standard rule refers to the order of operations:
- Brackets/Parentheses
- Orders (Exponents/Powers)
- Division and Multiplication (left to right)
- Addition and Subtraction (left to right)
Rule 5 in Math
Rule 5 refers to the fifth step in problem-solving:
- Read the problem
- Understand the given information
- Determine what's being asked
- Plan the solution
- Execute the plan and check the answer
Rule 3 in Math
Rule 3 refers to the distributive property:
a(b + c) = ab + ac
Basic Principles of Math
Reflexive Property
a = a
Symmetric Property
If a = b , then b = a
Transitive Property
If a = b and b = c , then a = c
Addition Property
If a = b , then a + c = b + c
Multiplication Property
If a = b , then a × c = b × c
Basic Math for Kids
Counting Rules
- Numbers go from left to right
- Each number has its own symbol
- Zero means nothing
Addition Rules
- Adding makes numbers bigger
- Order doesn't matter (2+3 = 3+2)
Subtraction Rules
- Subtraction makes numbers smaller
- Order matters (5-3 ≠ 3-5)
The Golden Rule of Algebra
What you do to one side of an equation, you must do to the other side to maintain equality.
The First Rule of Math
Two quantities that are equal remain equal when the same operation is performed on both.