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Questions and Answers
______ + (-) + (-) + ______ + ______ + (-______) =
______ + (-) + (-) + ______ + ______ + (-______) =
1
(-60) + (-11) + (-9) + 100 =
(-60) + (-11) + (-9) + 100 =
20
The additive inverse of (3 - 8) - (-4) is
The additive inverse of (3 - 8) - (-4) is
1
The sum of an integer and its additive inverse is always
The sum of an integer and its additive inverse is always
Match the following integers with their comparison:
Match the following integers with their comparison:
Simplify: -15 - (-40) =
Simplify: -15 - (-40) =
Simplify: 136 + (-127) =
Simplify: 136 + (-127) =
7 - (-8) =
7 - (-8) =
The additive inverse of a positive integer is always negative.
The additive inverse of a positive integer is always negative.
The sum of two integers is always positive.
The sum of two integers is always positive.
0 is a positive integer.
0 is a positive integer.
The sum of four different integers can never be zero.
The sum of four different integers can never be zero.
-1 is the greatest negative integer.
-1 is the greatest negative integer.
How far are two cyclists from each other after 20 minutes if one travels 1200 m downward and the other travels 350 m upward?
How far are two cyclists from each other after 20 minutes if one travels 1200 m downward and the other travels 350 m upward?
What is the position of a submarine floating at a depth of 640 m after ascending 230 m?
What is the position of a submarine floating at a depth of 640 m after ascending 230 m?
What was the temperature one month ago if it drops by 15 °C and the current temperature is -4 °C?
What was the temperature one month ago if it drops by 15 °C and the current temperature is -4 °C?
Which of the following statements is true regarding the closure property of addition?
Which of the following statements is true regarding the closure property of addition?
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Study Notes
Addition of Integers
- Add integers with like signs by adding their absolute values then applying the common sign
- Add integers with unlike signs by subtracting their absolute values (smaller from larger), then apply the sign of the integer with the larger absolute value
Additive Inverse
- For every integer a, there exists an opposite (-a) such that a + (-a) = 0
- a and -a are opposites or additive inverses of each other
Subtraction of Integers
- Subtraction is the inverse operation of addition
- To subtract an integer (b) from another (a), add the additive inverse of (b) to a: a - b = a + (-b)
Properties of Addition and Subtraction of Integers
- Closure Property of Addition: The sum of any two integers is an integer.
- Closure Property of Subtraction: The difference of any two integers is an integer
- Commutative Property of Addition: a + b = b + a
- Commutative Property of Subtraction: a - b ≠ b - a
- Associative Property of Addition: (a + b) + c = a + (b + c)
- Associative Property of Subtraction: (a - b) - c ≠ a - (b - c)
- Additive Identity Property: Add any integer to 0, and the sum is the integer: a + 0 = a
- Additive Inverse Property: Add any number to its additive inverse, and the sum is 0: a + (-a) = 0
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