Integer Operations Quiz

Integer Operations

• Integers are whole numbers, either positive, negative, or zero (..., -3, -2, -1, 0, 1, 2, 3, ...)
• There are five main integer operations: addition, subtraction, multiplication, division, and modulus (remainder)

Addition Of Integers

• Rules for adding integers:
  • Same sign: add the numbers and keep the same sign
    • Example: 3 + 2 = 5
  • Different signs: subtract the numbers and take the sign of the larger number
    • Example: 3 + (-2) = 1
    • Example: (-3) + 2 = -1
• Example problems:
  • 5 + 7 = 12
  • (-3) + 4 = 1
  • 2 + (-5) = -3

Subtraction Of Integers

• Rules for subtracting integers:
  • Same sign: subtract the numbers and keep the same sign
    • Example: 5 - 3 = 2
  • Different signs: add the numbers and take the sign of the first number
    • Example: 5 - (-3) = 8
    • Example: (-5) - 3 = -8
• Example problems:
  • 8 - 2 = 6
  • (-4) - (-3) = -1
  • 3 - 7 = -4

Properties Of Integers

• Commutative property: the order of integers does not change the result
  • Example: 2 + 3 = 3 + 2
  • Example: (-2) × 3 = 3 × (-2)
• Associative property: the order in which integers are grouped does not change the result
  • Example: (2 + 3) + 4 = 2 + (3 + 4)
  • Example: (2 × 3) × 4 = 2 × (3 × 4)
• Distributive property: multiplying an integer by a sum is the same as multiplying by each addend separately
  • Example: 2 × (3 + 4) = 2 × 3 + 2 × 4

Integer Word Problems

• Examples:
  • Tom has 5 apples and his friend gives him 2 more. How many apples does Tom have now?
    • Answer: 5 + 2 = 7
  • A bookshelf has 8 books on it. If 3 more books are added, how many books are on the bookshelf now?
    • Answer: 8 + 3 = 11
  • A bank account has a balance of -50.If50. If 50.If20 is deposited, what is the new balance?
    • Answer: (-50) + 20 = -30

Integers

• Integers are whole numbers, either positive, negative, or zero.

Addition of Integers

• When adding integers with the same sign, add the numbers and keep the same sign.
• When adding integers with different signs, subtract the numbers and take the sign of the larger number.
• Example problems:
  • 5 + 7 = 12
  • (-3) + 4 = 1
  • 2 + (-5) = -3

Subtraction of Integers

• When subtracting integers with the same sign, subtract the numbers and keep the same sign.
• When subtracting integers with different signs, add the numbers and take the sign of the first number.
• Example problems:
  • 8 - 2 = 6
  • (-4) - (-3) = -1
  • 3 - 7 = -4

Properties of Integers

Commutative Property

• The order of integers does not change the result.
• Example: 2 + 3 = 3 + 2
• Example: (-2) × 3 = 3 × (-2)

Associative Property

• The order in which integers are grouped does not change the result.
• Example: (2 + 3) + 4 = 2 + (3 + 4)
• Example: (2 × 3) × 4 = 2 × (3 × 4)

Distributive Property

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

Integer Word Problems

• Example: Tom has 5 apples and his friend gives him 2 more. He has 5 + 2 = 7 apples now.
• Example: A bookshelf has 8 books on it. If 3 more books are added, it has 8 + 3 = 11 books now.
• Example: A bank account has a balance of -$50. If $20 is deposited, the new balance is (-50) + 20 = -30.