Arithmetic Basics Quiz

Arithmetic

Definition: The branch of mathematics dealing with the properties and manipulation of numbers.
Basic Operations:
1. Addition (+): Combining two or more numbers to get a sum.
  - Properties:
    - Commutative: a + b = b + a
    - Associative: (a + b) + c = a + (b + c)
    - Identity: a + 0 = a
2. Subtraction (−): Finding the difference between two numbers.
  - Not commutative or associative.
  - Inverse of addition: a - b = a + (-b)
3. Multiplication (×): Repeated addition of a number.
  - Properties:
    - Commutative: a × b = b × a
    - Associative: (a × b) × c = a × (b × c)
    - Identity: a × 1 = a
    - Distributive: a × (b + c) = a × b + a × c
4. Division (÷): Splitting a number into equal parts.
  - Inverse of multiplication: a ÷ b = a × (1/b)
  - Not commutative or associative.
Order of Operations:
- PEMDAS/BODMAS:
  - Parentheses/Brackets
  - Exponents/Orders (Powers and Roots)
  - Multiplication and Division (from left to right)
  - Addition and Subtraction (from left to right)
Properties of Numbers:
- Even Numbers: Divisible by 2.
- Odd Numbers: Not divisible by 2.
- Prime Numbers: Greater than 1, divisible only by 1 and themselves.
- Composite Numbers: Greater than 1, divisible by additional numbers beyond 1 and itself.
Fractions:
- Definition: Part of a whole, expressed as a/b.
- Types:
  - Proper: a < b
  - Improper: a ≥ b
  - Mixed: Combination of whole number and a proper fraction.
- Operations:
  - Addition/Subtraction: Find common denominator.
  - Multiplication: a/b × c/d = (a × c)/(b × d)
  - Division: a/b ÷ c/d = a/b × d/c
Decimals:
- Definition: A fraction expressed in a base-10 format.
- Operations: Same as whole numbers but align decimal points.
Percentage:
- A way of expressing a number as a fraction of 100.
- Calculation: (part/whole) × 100%.
Estimation:
- Rounding numbers to make calculations easier and quicker.
- Useful for checking reasonableness of answers.
Applications:
- Everyday calculations (budgeting, shopping).
- Measurement and data analysis.
- Problem-solving in various fields (science, engineering).

Arithmetic Overview

Arithmetic focuses on the properties and manipulation of numbers, essential for everyday calculations and advanced mathematics.

Basic Operations

Addition (+): Combines two or more numbers to produce a sum.
- Properties:
  - Commutative: a + b = b + a
  - Associative: (a + b) + c = a + (b + c)
  - Identity: a + 0 = a
Subtraction (−): Determines the difference between numbers.
- Not commutative or associative; serves as the inverse of addition: a - b = a + (-b).
Multiplication (×): Functions as repeated addition of a number.
- Properties:
  - Commutative: a × b = b × a
  - Associative: (a × b) × c = a × (b × c)
  - Identity: a × 1 = a
  - Distributive: a × (b + c) = a × b + a × c
Division (÷): Divides a number into equal parts.
- Inverse of multiplication: a ÷ b = a × (1/b); also, not commutative or associative.

Order of Operations

Use PEMDAS/BODMAS for solving expressions:
- Parentheses/Brackets
- Exponents/Orders (Powers and Roots)
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)

Properties of Numbers

Even Numbers: Numbers divisible by 2.
Odd Numbers: Numbers not divisible by 2.
Prime Numbers: Greater than 1 and divisible only by 1 and themselves.
Composite Numbers: Greater than 1, divisible by additional numbers besides 1 and itself.

Fractions

Definition: Represents a part of a whole as a/b.
Types:
- Proper: Numerator (a) < Denominator (b)
- Improper: Numerator (a) ≥ Denominator (b)
- Mixed: Combination of whole number and proper fraction.
Operations:
- Addition/Subtraction: Use common denominators to combine.
- Multiplication: a/b × c/d = (a × c)/(b × d)
- Division: a/b ÷ c/d = a/b × d/c