## Questions and Answers

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

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

What is the commutative property of integers?

What is the result of 4 × (-2)?

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

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What is the associative property of integers?

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

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

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What is the distributive property of integers?

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 If $15 is withdrawn, what is the new balance?

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## 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

- Same sign: add the numbers and keep the same sign
- 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

- Same sign: subtract the numbers and keep the same sign
- 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

- Tom has 5 apples and his friend gives him 2 more. How many apples does Tom have now?

### 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.

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## Description

Test your knowledge of integer operations including addition, subtraction, multiplication, division, and modulus. Learn the rules for adding integers with same and different signs.