Integer Operations Quiz

Questions and Answers

What is the result of 2 + (-3)?

-1 (correct)

-5

What is the result of (-5) - 3?

-2

-8 (correct)

What is the commutative property of integers?

the order of integers does not change the result (correct)

only applies to addition

only applies to multiplication

the order of integers always changes the result

What is the result of 4 × (-2)?

-8 Signup and view all the answers

Tom has 8 apples and gives 2 to his friend. How many apples does Tom have now?

6 Signup and view all the answers

What is the associative property of integers?

the order in which integers are grouped does not change the result Signup and view all the answers

What is the result of (-2) + 5?

3 Signup and view all the answers

A bookshelf has 5 books on it. If 2 more books are removed, how many books are on the bookshelf now?

3 Signup and view all the answers

What is the distributive property of integers?

multiplying an integer by a sum is the same as multiplying by each addend separately Signup and view all the answers

A bank account has a balance of -$20. If $15 is withdrawn, what is the new balance?

-$35 Signup and view all the answers

Study Notes

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.