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Questions and Answers
What is the result of 5 + (-2)?
What is the result of (-3) × 4?
What is the result of (-2) ÷ (-4)?
What is the result of 8 - (-3)?
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What is the correct order of operations for the expression 2 × 3 + 12 - 8?
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What is the result of 9 - 4 + (-2)?
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What is the result of a + (-a) in integer properties?
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Which property states that the order of integers does not change the result?
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Which property is demonstrated by the equation (a × b) × c = a × (b × c)?
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What is the multiplicative identity in integer properties?
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Which property is demonstrated by the equation a × (b + c) = a × b + a × c?
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What is the additive inverse of an integer a in integer properties?
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Study Notes
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:
- Parentheses (if present)
- Exponents (if present)
- Multiplication and Division (from left to right)
- 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
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Description
Test your understanding of adding and subtracting integers with same and different signs.
