JAMB Mathematics Mind Map - Arithmetic PDF

# Learn Shortcuts, and Fast Mental Math Techniques ## Arithmetic - Practical Steps for Arithmetic - Core Concept of Arithmetic - First Principles of Arithmetic **Arithmetic uses "modifiers" standardly known as "operators" (i.e. + - * /) to modify the values (or numbers) they are applied to.**...

# Learn Shortcuts, and Fast Mental Math Techniques ## Arithmetic - Practical Steps for Arithmetic - Core Concept of Arithmetic - First Principles of Arithmetic **Arithmetic uses "modifiers" standardly known as "operators" (i.e. + - * /) to modify the values (or numbers) they are applied to.** ## Number (Values) - **Natural Numbers:** This are numbers from the regular counting system e.g. 1, 2, 3, 4, 5, 6, 7,.... and so on. They can only be positive. - **Whole Numbers:** Also numbers from the regular counting system but starting from Zero (0) e.g. 0, 1, 2, 3, 4, 5, 6, 7,.... and so on. They can only be positive also. - **Integers:** These are both negative and positive numbers from the regular starting from Zero (0) e.g. -3, -2, -1, 0, 1, 2, 3, 4, 5.... and so on. - **Rational Numbers:** These are both negative and positive “fractional numbers”, where the numerator and denominator are both Integers, except the denominator is never Zero (0). - **Irrational Numbers:** These are both negative and positive “fractional numbers”, where the numerator and denominator are both Integers, except the denominator is never Zero (0). ## Modifiers (Operators) - **Addition (+):** This modifies the values it is applied by “combining the quantity of these values”. - **Subtraction (-):** This modifies an original value by subtracting with a reference value; the result is also the difference of both values. - **Multiplication (* or ×) or ×:** This modifies an original value by adding the reference value by its exact quantity. - **Division (/) or ÷):** This modifies an original value by separating the exact quantity of the reference value from it. - **Secondary or Advanced Modifiers (or Operator):** Many Secondary or Advanced modifier (or operation) will be a combination of the basic or semi-basic modifiers, while some will be original. ## Properties of Modifiers (or Operator) - **Commutative Property or “The Order Does Not Matter” Property:** a + b = b + a also a × b = b × a. This applies to only the Addition and Multiplication modifiers. Where a and b can be either entities (variables) or numbers (values). - **Associative Property or “The Group Does Not Matter” Property:** (a + b) + c = (b + a) + c. This applies to only the Addition and Multiplication modifiers. Where a, b, c can be either entities (variables) or values (numbers). - **Distributive Property or “The Sharing” Property:** a × (b + c) = a × b + a × c. This means you can share (distribute) the multiplication modifier across where addition modifier is applied within a parentheses of entities (variables) or values (numbers). - **Other Properties and Secondary or Advanced modifier (Operator) Properties.** You must realize there other modifier (operators) properties for basic modifiers (operators) as well as for Secondary or Advanced modifiers (operators).