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Questions and Answers
What is the result of dividing a negative integer by a positive integer?
What is the result of dividing a negative integer by a positive integer?
What is the quotient of (–100) ÷ 5?
What is the quotient of (–100) ÷ 5?
Which of the following represents the property of division for negative integers correctly?
Which of the following represents the property of division for negative integers correctly?
If (–8) × (–9) equals 72, what is the corresponding division statement?
If (–8) × (–9) equals 72, what is the corresponding division statement?
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How do you represent (–45) ÷ 5?
How do you represent (–45) ÷ 5?
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What is the result of dividing a negative integer by 1?
What is the result of dividing a negative integer by 1?
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How is division not commutative for integers demonstrated?
How is division not commutative for integers demonstrated?
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What happens when you divide any integer by (–1)?
What happens when you divide any integer by (–1)?
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Which statement about dividing by zero is true?
Which statement about dividing by zero is true?
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What can you conclude from the example (–8) ÷ (–4) = 2?
What can you conclude from the example (–8) ÷ (–4) = 2?
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Study Notes
Division of Integers
- Division is not commutative for integers, meaning ( a ÷ b \neq b ÷ a ).
- Example: ( (–8) ÷ (–4) = 2 ) while ( (–4) ÷ (–8) \neq 2 ).
- Division of integers can yield different types of results:
- ( a ÷ 0 ) is undefined; ( 0 ÷ b = 0 ) for any ( b \neq 0 ).
Division by One
- Dividing any integer by ( 1 ) results in the same integer.
- Example: ( (–8) ÷ 1 = (–8) ).
- This rule holds true for negative integers as well.
Division by Negative One
- Dividing an integer by ( –1 ) changes the sign of the integer.
- Example: ( (–1) × 5 = –5 ) implies ( 5 ÷ (–1) = (–5) ).
Inverse Relationship with Multiplication
- Division is the inverse operation of multiplication.
- Example: For ( 3 × 5 = 15 ), it follows that ( 15 ÷ 5 = 3 ) and ( 15 ÷ 3 = 5 ).
- Each multiplication statement corresponds to two division statements.
Observations on Division Results
- When dividing a negative integer by a positive integer, the quotient is negative.
- Example: ( (–32) ÷ 4 = (–8) ).
- Conversely, dividing a positive integer by a negative integer also results in a negative quotient.
Negative Divisions
- Dividing two negative integers results in a positive quotient.
- Example: ( (–12) ÷ (–6) = 2 ).
General Division Rules
- For two positive integers ( a ) and ( b ):
- ( a ÷ (–b) = (–a) ÷ b ) for ( b \neq 0 ).
- ( (–a) ÷ (–b) = a ÷ b ) for ( b \neq 0 ).
Non-closure Property
- Integers are not closed under division, as not every division operation yields another integer.
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Description
Test your knowledge of division with negative numbers in this algebra quiz. Analyze statements and inferences to determine the outcomes of various division operations. Perfect for students looking to reinforce their understanding of integer results.
