Questions and Answers
Que es un Algebraic Proof?
Define la Addition Property of Equality.
Si a = b, entonces a + c = b + c.
Define la Subtraction Property of Equality.
Si a = b, entonces a - c = b - c.
Define la Multiplication Property of Equality.
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Define la Division Property of Equality.
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La Reflexive Property of Equality dice que a = b.
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Define la Symmetric Property of Equality.
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Define la Transitive Property of Equality.
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Define la Substitution Property of Equality.
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Define el Distributive Property.
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Define un Two-Column / Formal Proof.
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Study Notes
Algebraic Proof
- Composed of a series of algebraic properties used to demonstrate the validity of statements.
Addition Property of Equality
- Establishes that adding the same value to both sides of an equation maintains equality: if a = b, then a + c = b + c.
Subtraction Property of Equality
- States that subtracting the same value from both sides of an equation preserves equality: if a = b, then a - c = b - c.
Multiplication Property of Equality
- Indicates that multiplying both sides of an equation by the same non-zero value keeps equality intact: if a = b, then a × c = b × c.
Division Property of Equality
- Asserts that dividing both sides of an equation by the same non-zero value maintains equality: if a = b and c ≠ 0, then a ÷ c = b ÷ c.
Reflexive Property of Equality
- Confirms that any quantity is equal to itself: a = a.
Symmetric Property of Equality
- Demonstrates that if one quantity equals another, the reverse is also true: if a = b, then b = a.
Transitive Property of Equality
- Describes the relationship among three quantities: if a = b and b = c, then it follows that a = c.
Substitution Property of Equality
- Allows for the replacement of one quantity with another in expressions or equations when they are known to be equal: if a = b, a can be substituted for b.
Distributive Property
- Facilitates the distribution of multiplication over addition: a(b + c) = ab + ac.
Two-Column / Formal Proof
- A structured form of proof that organizes statements and reasons into two distinct columns for clarity.
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Description
This quiz focuses on various algebraic proofs and their properties. It covers key concepts such as the Addition, Subtraction, Multiplication, and Division Properties of Equality. Test your knowledge on these fundamental algebraic principles.
