Whole Numbers and Operations

Whole Numbers

• A set of numbers that includes all positive integers, including 0
• Example: 0, 1, 2, 3, ...

Operations with Whole Numbers

• Addition: combining two or more whole numbers to get a total or a sum
• Subtraction: finding the difference between two whole numbers
• Multiplication: repeating a whole number a certain number of times to get a product
• Division: sharing a whole number into equal parts or groups

Properties of Operations

• Commutative Property: the order of numbers does not change the result
  • 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)
• Distributive Property: multiplying a number by a sum is the same as multiplying by each addend separately
  • Example: 2 × (3 + 4) = 2 × 3 + 2 × 4

Place Value

• Ones Place: the rightmost digit in a number, representing individual units
• Tens Place: the digit to the left of the ones place, representing groups of 10
• Hundreds Place: the digit to the left of the tens place, representing groups of 100
• Thousands Place: the digit to the left of the hundreds place, representing groups of 1000

Rounding Numbers

• Rounding Down: rounding a number to the nearest whole number by dropping the decimal part
• Rounding Up: rounding a number to the nearest whole number by adding 1 to the whole number part if the decimal part is 0.5 or greater

Whole Numbers

• A set of numbers including all positive integers and 0
• Examples: 0, 1, 2, 3, ...

Operations with Whole Numbers

• Addition: combining whole numbers to get a total or sum
• Subtraction: finding the difference between whole numbers
• Multiplication: repeating a whole number a certain number of times to get a product
• Division: sharing a whole number into equal parts or groups

Properties of Operations

Commutative Property

• The order of numbers does not change the result
• 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)

Distributive Property

• Multiplying a number by a sum is the same as multiplying by each addend separately
• Example: 2 × (3 + 4) = 2 × 3 + 2 × 4

Place Value

Ones Place

• Rightmost digit in a number, representing individual units

Tens Place

• Digit to the left of the ones place, representing groups of 10

Hundreds Place

• Digit to the left of the tens place, representing groups of 100

Thousands Place

• Digit to the left of the hundreds place, representing groups of 1000

Rounding Numbers

Rounding Down

• Rounding a number to the nearest whole number by dropping the decimal part

Rounding Up

• Rounding a number to the nearest whole number by adding 1 to the whole number part if the decimal part is 0.5 or greater