Podcast
Questions and Answers
What is the result of 5 + (-2)?
What is the result of 5 + (-2)?
What is the result of (-3) × 4?
What is the result of (-3) × 4?
What is the result of (-2) ÷ (-4)?
What is the result of (-2) ÷ (-4)?
What is the result of 8 - (-3)?
What is the result of 8 - (-3)?
Signup and view all the answers
What is the correct order of operations for the expression 2 × 3 + 12 - 8?
What is the correct order of operations for the expression 2 × 3 + 12 - 8?
Signup and view all the answers
What is the result of 9 - 4 + (-2)?
What is the result of 9 - 4 + (-2)?
Signup and view all the answers
What is the result of a + (-a) in integer properties?
What is the result of a + (-a) in integer properties?
Signup and view all the answers
Which property states that the order of integers does not change the result?
Which property states that the order of integers does not change the result?
Signup and view all the answers
Which property is demonstrated by the equation (a × b) × c = a × (b × c)?
Which property is demonstrated by the equation (a × b) × c = a × (b × c)?
Signup and view all the answers
What is the multiplicative identity in integer properties?
What is the multiplicative identity in integer properties?
Signup and view all the answers
Which property is demonstrated by the equation a × (b + c) = a × b + a × c?
Which property is demonstrated by the equation a × (b + c) = a × b + a × c?
Signup and view all the answers
What is the additive inverse of an integer a in integer properties?
What is the additive inverse of an integer a in integer properties?
Signup and view all the answers
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
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of adding and subtracting integers with same and different signs.
