Basic Number Operations

Number Operations

• Addition: combining two or more numbers to get a total or a sum
  • Example: 2 + 3 = 5
• Subtraction: finding the difference between two numbers
  • Example: 5 - 2 = 3
• Multiplication: repeating a number a certain number of times to get a product
  • Example: 2 × 3 = 6
• Division: sharing a number into equal parts or groups
  • Example: 6 ÷ 2 = 3

Properties of Arithmetic Operations

• Commutative Property: the order of numbers does not change the result
  • Example: 2 + 3 = 3 + 2
  • Example: 2 × 3 = 3 × 2
• Associative Property: the order in which numbers are grouped does not change the result
  • Example: (2 + 3) + 4 = 2 + (3 + 4)
  • Example: (2 × 3) × 4 = 2 × (3 × 4)
• Distributive Property: a number can be distributed to multiple numbers
  • Example: 2 × (3 + 4) = 2 × 3 + 2 × 4

Order of Operations

• PEMDAS: a mnemonic to remember the order of operations
  1. Parentheses: evaluate expressions inside parentheses first
  2. Exponents: evaluate any exponential expressions next
  3. Multiplication and Division: evaluate from left to right
  4. Addition and Subtraction: evaluate from left to right

Arithmetic Concepts

• Place Value: the value of a digit based on its position in a number
  • Example: in the number 456, the 4 is in the hundreds place, the 5 is in the tens place, and the 6 is in the ones place
• Rounding: approximating a number to a nearby value
  • Example: rounding 4.7 to the nearest whole number is 5

Number Operations

• Addition is the process of combining two or more numbers to get a total or a sum, e.g. 2 + 3 = 5.
• Subtraction is the process of finding the difference between two numbers, e.g. 5 - 2 = 3.
• Multiplication is the process of repeating a number a certain number of times to get a product, e.g. 2 × 3 = 6.
• Division is the process of sharing a number into equal parts or groups, e.g. 6 ÷ 2 = 3.

Properties of Arithmetic Operations

• Commutative Property states that the order of numbers does not change the result, e.g. 2 + 3 = 3 + 2, and 2 × 3 = 3 × 2.
• Associative Property states that the order in which numbers are grouped does not change the result, e.g. (2 + 3) + 4 = 2 + (3 + 4), and (2 × 3) × 4 = 2 × (3 × 4).
• Distributive Property states that a number can be distributed to multiple numbers, e.g. 2 × (3 + 4) = 2 × 3 + 2 × 4.

Order of Operations

• PEMDAS is a mnemonic to remember the order of operations:
  • Evaluate expressions inside Parentheses first.
  • Evaluate any Exponents next.
  • Evaluate Multiplication and Division from left to right.
  • Evaluate Addition and Subtraction from left to right.

Arithmetic Concepts

• Place Value is the value of a digit based on its position in a number, e.g. in the number 456, the 4 is in the hundreds place, the 5 is in the tens place, and the 6 is in the ones place.
• Rounding is approximating a number to a nearby value, e.g. rounding 4.7 to the nearest whole number is 5.