Questions and Answers
What is the result of (–10) + 3?
–7
What is the result of (–75) + 18?
–57
What is the result of 27 + (–27)?
0
What is the result of (______) + 0?
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What is the result of (–35) + (–10)?
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What is the result of 17 – (–21)?
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What is the result of (–21) – (–10)?
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What is the result of 32 – (–17)?
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What is the result of (–18) – (–18)?
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What is the result of (______) – 0?
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The sum of two integers is always an integer.
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Addition is associative for integers.
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Addition is commutative for integers.
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Subtraction is commutative for integers.
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Integers are closed under subtraction.
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Study Notes
Properties of Integers
Closure under Addition
- The addition of any two integers results in another integer, demonstrating closure under addition.
- Examples include:
- 17 + 23 = 40 (integer)
- (–10) + 3 is an integer
- (–75) + 18 is an integer
- 19 + (–25) = –6 (integer)
- 27 + (–27) = 0 (integer)
- (–20) + 0 is an integer
- (–35) + (–10) is an integer
- Thus, for any integers a and b, a + b is always an integer.
Closure under Subtraction
- The subtraction of two integers results in another integer, indicating closure under subtraction.
- Examples include:
- 7 – 9 = –2 (integer)
- (–8) – (–14) = 6 (integer)
- Other shown subtractions (e.g., 17 – (–21)) lead to integers.
- Concludes that for any integers a and b, a – b is also an integer.
Commutative Property
- Addition of integers is commutative; a + b = b + a is valid.
- Examples that confirm commutativity:
- 5 + (–6) = (–6) + 5 = –1
- (–8) + (–9) = (–9) + (–8)
- (–23) + 32 = 32 + (–23)
- Subtraction, however, is not commutative; a – b ≠ b – a generally holds true.
- Examples illustrating non-commutativity:
- 5 – (–3) = 8, but (–3) – 5 = –8.
Associative Property
- Addition of integers is associative; (a + b) + c = a + (b + c).
- Examples showcasing associativity:
- ((–5) + (–3)) + (–2) results in the same sum as (–5) + ((–3) + (–2)).
- Other combinations verify this property consistently.
- Closure of results under different groupings confirms that addition is associative for integers.
Summary
- Closure properties of integers affirm that both addition and subtraction yield integers.
- Commutative property holds for addition, while subtraction does not exhibit this property.
- Associative property is valid for addition of integers.
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Description
Explore the properties of addition and subtraction of integers in this quiz. This covers the concept of closure under addition, highlighting how the sum of two integers results in another integer. Test your understanding of these foundational math concepts with engaging questions.
