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Questions and Answers
What is the result of the expression $-8 - (-5) + 2 \times (-3)$?
What is the result of the expression $-8 - (-5) + 2 \times (-3)$?
- -7
- -1
- 1
- -9 (correct)
The expression $-5 \times (2 + (-2))$ results in a positive number.
The expression $-5 \times (2 + (-2))$ results in a positive number.
False (B)
What integer, when added to -12, results in 5?
What integer, when added to -12, results in 5?
17
According to the order of operations, in the expression $3 + 4 \times 2$, the ________ operation should be performed first.
According to the order of operations, in the expression $3 + 4 \times 2$, the ________ operation should be performed first.
Match the integer operation with its corresponding property:
Match the integer operation with its corresponding property:
What is the quotient of $-48 \div (-6)$?
What is the quotient of $-48 \div (-6)$?
Subtracting a negative integer from another integer always results in a smaller value than the original integer.
Subtracting a negative integer from another integer always results in a smaller value than the original integer.
What is the additive inverse of -15?
What is the additive inverse of -15?
The product of a negative integer and a positive integer is always a ________ integer.
The product of a negative integer and a positive integer is always a ________ integer.
Which property is demonstrated by the equation $(3 + (-2)) + 5 = 3 + (-2 + 5)$?
Which property is demonstrated by the equation $(3 + (-2)) + 5 = 3 + (-2 + 5)$?
Flashcards
What are integers?
What are integers?
Whole numbers that can be positive, negative, or zero.
Adding integers with the same sign
Adding integers with the same sign
Add their absolute values and keep the common sign.
Adding integers with different signs
Adding integers with different signs
Find the difference between their absolute values and use the sign of the larger absolute value.
What is an additive inverse?
What is an additive inverse?
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Subtracting an integer
Subtracting an integer
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Positive × Positive
Positive × Positive
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Negative × Negative
Negative × Negative
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Positive × Negative
Positive × Negative
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What is the order of operations?
What is the order of operations?
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Commutative Property
Commutative Property
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Study Notes
Integers
- Integers include positive whole numbers, negative whole numbers, and zero
- Positive integers are greater than zero such as 1, 2, 3, etc.
- Negative integers are less than zero such as -1, -2, -3, etc.
- Zero is neither positive nor negative
Addition of Integers
- Adding integers combines their values
- To add integers sharing the same sign:
- Add their absolute values together
- Retain the sign they have in common
- Example: (+3) + (+5) = +8
- Example: (-2) + (-4) = -6
- To add integers with different signs:
- Find the difference between their absolute values
- Use the sign of the integer with the greater absolute value
- Example: (+7) + (-3) = +4 because |+7| > |-3|
- Example: (-9) + (+2) = -7 because |-9| > |+2|
- The additive inverse, or opposite, of integer 'a' is '-a,' and their sum equals zero: a + (-a) = 0
- Example: 5 + (-5) = 0
Subtraction of Integers
- Subtracting an integer equals adding its additive inverse
- To subtract integer 'b' from integer 'a,' change 'b' to '-b' and add it to 'a': a - b = a + (-b)
- Example: (+5) - (+2) = (+5) + (-2) = +3
- Example: (+3) - (-4) = (+3) + (+4) = +7
- Example: (-6) - (+1) = (-6) + (-1) = -7
- Example: (-2) - (-5) = (-2) + (+5) = +3
Multiplication of Integers
- When multiplying integers, resulting sign depends on the signs of the integers
- Positive × Positive = Positive
- Example: (+3) × (+4) = +12
- Negative × Negative = Positive
- Example: (-2) × (-5) = +10
- Positive × Negative = Negative
- Example: (+6) × (-1) = -6
- Negative × Positive = Negative
- Example: (-4) × (+3) = -12
- Positive × Positive = Positive
- If the signs are the same, the product is positive
- If the signs are different, the product is negative
Division of Integers
- Division rules mirror those of multiplication regarding the sign
- Positive ÷ Positive = Positive
- Example: (+10) ÷ (+2) = +5
- Negative ÷ Negative = Positive
- Example: (-8) ÷ (-4) = +2
- Positive ÷ Negative = Negative
- Example: (+15) ÷ (-3) = -5
- Negative ÷ Positive = Negative
- Example: (-20) ÷ (+5) = -4
- Positive ÷ Positive = Positive
- Same signs yield a positive quotient
- Different signs yield a negative quotient
- Division by zero is undefined
Order of Operations
- With expressions involving multiple operations, follow the order of operations (PEMDAS/BODMAS)
- Parentheses/Brackets
- Exponents/Orders
- Multiplication and Division (left to right)
- Addition and Subtraction (left to right)
- Example: 2 + 3 × (-4)
- First, multiplication: 3 × (-4) = -12
- Then, addition: 2 + (-12) = -10
- Example: (5 - 7) ÷ (-2) + 1
- First, simplify parentheses: (5 - 7) = -2
- Then, division: (-2) ÷ (-2) = +1
- Finally, addition: 1 + 1 = 2
Properties of Integer Operations
- Commutative Property: Applies to addition and multiplication
- a + b = b + a
- Example: 2 + (-3) = -3 + 2
- a × b = b × a
- Example: (-4) × 5 = 5 × (-4)
- a + b = b + a
- Associative Property: Applies to addition and multiplication
- (a + b) + c = a + (b + c)
- Example: (1 + (-2)) + 3 = 1 + (-2 + 3)
- (a × b) × c = a × (b × c)
- Example: ((-1) × 2) × 3 = (-1) × (2 × 3)
- (a + b) + c = a + (b + c)
- Distributive Property:
- a × (b + c) = (a × b) + (a × c)
- Example: 2 × (3 + (-4)) = (2 × 3) + (2 × (-4))
- a × (b + c) = (a × b) + (a × c)
- Identity Property:
- Additive Identity: a + 0 = a
- Example: -5 + 0 = -5
- Multiplicative Identity: a × 1 = a
- Example: 7 × 1 = 7
- Additive Identity: a + 0 = a
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