Integer Operations Quiz

Integer Operations

Addition of Integers

• Rules:
  • Same signs: Add the numbers and keep the same sign
  • Different signs: Subtract the smaller number from the larger number and keep the sign of the larger number
• Examples:
  • 2 + 3 = 5 (same signs)
  • 2 + (-3) = -1 (different signs)
  • (-2) + 3 = 1 (different signs)

Subtraction of Integers

• Rules:
  • Subtracting a positive number is the same as adding a negative number
  • Subtracting a negative number is the same as adding a positive number
• Examples:
  • 4 - 2 = 2 (subtracting a positive number)
  • 4 - (-2) = 6 (subtracting a negative number)
  • (-4) - 2 = -6 (subtracting a positive number)

Multiplication of Integers

• Rules:
  • Same signs: Multiply the numbers and the result is positive
  • Different signs: Multiply the numbers and the result is negative
• Examples:
  • 2 × 3 = 6 (same signs)
  • 2 × (-3) = -6 (different signs)
  • (-2) × 3 = -6 (different signs)

Division of Integers

• Rules:
  • Same signs: Divide the numbers and the result is positive
  • Different signs: Divide the numbers and the result is negative
• Examples:
  • 6 ÷ 2 = 3 (same signs)
  • 6 ÷ (-2) = -3 (different signs)
  • (-6) ÷ 2 = -3 (different signs)

Order of Operations

• When performing multiple operations, follow the order:
  1. Parentheses (if present)
  2. Exponents (if present)
  3. Multiplication and Division (from left to right)
  4. Addition and Subtraction (from left to right)

Integer Operations

Addition of Integers

• Same signs: Add numbers and keep the same sign
• Different signs: Subtract the smaller number from the larger number and keep the sign of the larger number
• Addition is commutative: 2 + 3 = 3 + 2
• Addition is associative: (2 + 3) + 4 = 2 + (3 + 4)

Subtraction of Integers

• Subtracting a positive number is the same as adding a negative number
• Subtracting a negative number is the same as adding a positive number
• Subtraction is not commutative: 2 - 3 ≠ 3 - 2

Multiplication of Integers

• Same signs: Multiply numbers and the result is positive
• Different signs: Multiply numbers and the result is negative
• Multiplication is commutative: 2 × 3 = 3 × 2
• Multiplication is associative: (2 × 3) × 4 = 2 × (3 × 4)

Division of Integers

• Same signs: Divide numbers and the result is positive
• Different signs: Divide numbers and the result is negative
• Division is not commutative: 6 ÷ 2 ≠ 2 ÷ 6
• Division by zero is undefined

Order of Operations

• Follow the order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)
• Evaluate expressions from top to bottom and left to right
• Use parentheses to group numbers and operations when necessary

Integer Properties

Commutative Property

• The order of integers does not affect the result of addition and multiplication.
• Addition: a + b = b + a
• Multiplication: a × b = b × a

Associative Property

• The order of grouping integers does not change the result of addition and multiplication.
• Addition: (a + b) + c = a + (b + c)
• Multiplication: (a × b) × c = a × (b × c)

Distributive Property

• Multiplication distributes over addition.
• a × (b + c) = a × b + a × c

Identity Properties

Additive Identity

• 0 is the additive identity, as it does not change the result when added to an integer.
• a + 0 = a

Multiplicative Identity

• 1 is the multiplicative identity, as it does not change the result when multiplied by an integer.
• a × 1 = a

Inverse Properties

Additive Inverse

• The additive inverse of an integer is the integer that, when added, results in 0.
• The additive inverse of a is -a, since a + (-a) = 0

Multiplicative Inverse

• The multiplicative inverse of an integer is the integer that, when multiplied, results in 1.
• The multiplicative inverse of a (if it exists) is 1/a, since a × (1/a) = 1

Test your understanding of adding and subtracting integers with same and different signs.