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Questions and Answers
What does the reflexive property of equality state?
What does the reflexive property of equality state?
- For all real numbers a, a = a (correct)
- For all real numbers a and b, if a = b, then b = a
- For all real numbers a, b, and c, if a = b and b = c, then a = c
- For all real numbers a, b, and c, if a = b then a + c = b + c
What does the symmetric property of equality state?
What does the symmetric property of equality state?
- For all real numbers a and b, if a = b, then b = a (correct)
- For all real numbers a, a = a
- For all real numbers a, b, and c, if a = b then a + c = b + c
- For all real numbers a, b, and c, if a = b and b = c, then a = c
What does the transitive property of equality state?
What does the transitive property of equality state?
- For all real numbers a, b, and c, if a = b then a + c = b + c
- For all real numbers a and b, if a = b, then b = a
- For all real numbers a, b, and c, if a = b and b = c, then a = c (correct)
- For all real numbers a, a = a
What does the addition property of equality state?
What does the addition property of equality state?
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What does the subtraction property of equality state?
What does the subtraction property of equality state?
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What does the multiplication property of equality state?
What does the multiplication property of equality state?
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What does the division property of equality state?
What does the division property of equality state?
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Study Notes
Properties of Equality
- Reflexive Property of Equality: Any real number is equal to itself, expressed as ( a = a ).
- Symmetric Property of Equality: If one real number equals another, the reverse is also true; if ( a = b ), then ( b = a ).
- Transitive Property of Equality: A chain of equalities leads to a conclusion of equality; if ( a = b ) and ( b = c ), then ( a = c ).
Addition and Subtraction Properties
- Addition Property of Equality: If two numbers are equal, adding the same number to both sides maintains the equality; if ( a = b ), then ( a + c = b + c ).
- Subtraction Property of Equality: Similar to addition, subtracting the same number from both sides of an equation preserves equality; if ( a = b ), then ( a - c = b - c ).
Multiplication and Division Properties
- Multiplication Property of Equality: Multiplying both sides of an equality by the same non-zero number keeps the equality intact; if ( a = b ), then ( ac = bc ).
- Division Property of Equality: Dividing both sides of an equality by the same non-zero number maintains equality; if ( a = b ) and ( c \neq 0 ), then ( \frac{a}{c} = \frac{b}{c} ).
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