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Algebra Properties Flashcards
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Algebra Properties Flashcards

Created by
@MatchlessAltoSaxophone

Questions and Answers

What is the Addition Property of Equality?

  • IF a=b THEN a+c=b+c (correct)
  • a+0=a
  • IF a=b THEN a*c=b*c
  • a+(-a)=0

    • What does the Additive Identity Property state?

    a+0=a

    What is the Additive Inverse Property?

    a+(-a)=0

    What does the Associative Property of Addition indicate?

    <p>(a+b)+c=a+(b+c)</p> Signup and view all the answers

    What is the Associative Property of Multiplication?

    <p>(a<em>b)<em>c=a</em>(b</em>c)</p> Signup and view all the answers

    What does the Commutative Property of Addition state?

    <p>a+b=b+a</p> Signup and view all the answers

    What is the Commutative Property of Multiplication?

    <p>a<em>b=b</em>a</p> Signup and view all the answers

    What does the Distributive Property of Multiplication over Addition/Subtraction express?

    <p>a(b+c)=a<em>b+a</em>c AND a(b-c)=a<em>b-a</em>c</p> Signup and view all the answers

    What does the Division Property of Equality state?

    <p>a/c=b/c IF a=b</p> Signup and view all the answers

    What is the Multiplication Property of Equality?

    <p>IF a=b THEN a<em>c=b</em>c</p> Signup and view all the answers

    What does the Multiplicative Identity Property state?

    <p>1*a=a</p> Signup and view all the answers

    What is the Multiplicative Inverse Property?

    <p>a*1/a=1</p> Signup and view all the answers

    What does the Substitution Property assert?

    <p>IF a=b THEN EITHER ONE CAN BE SUBSTITUTED FOR THE OTHER</p> Signup and view all the answers

    What is the Subtraction Property of Equality?

    <p>IF a=b THEN a-c=b-c</p> Signup and view all the answers

    What does the Transitive Property of Equality state?

    <p>IF a=b AND b=c THEN a=c</p> Signup and view all the answers

    What is the Zero Product Property?

    <p>IF a*b=0 THEN a=0, b=0, OR BOTH EQUAL ZERO</p> Signup and view all the answers

    Study Notes

    Algebraic Proofs Properties

    • Addition Property of Equality: If two quantities are equal, adding the same value to both retains equality.

    • Additive Identity Property: Adding zero to any number leaves the number unchanged.

    • Additive Inverse Property: The sum of a number and its opposite (negative) is zero.

    • Associative Property of Addition: Changing the grouping of numbers in addition does not affect the sum.

    • Associative Property of Multiplication: Changing the grouping of factors in multiplication does not affect the product.

    • Commutative Property of Addition: The order of adding two numbers can be switched without changing the result.

    • Commutative Property of Multiplication: The order of multiplying two numbers can be switched without changing the product.

    • Distributive Property: Multiplying a number by a sum or difference can be done by distributing the multiplier to each term within the parentheses.

    • Division Property of Equality: If two quantities are equal, dividing both by the same non-zero value preserves equality.

    • Multiplication Property of Equality: If two quantities are equal, multiplying both by the same value retains equality.

    • Multiplicative Identity Property: Multiplying any number by one results in the original number.

    • Multiplicative Inverse Property: Any number multiplied by its reciprocal equals one.

    • Substitution Property: Equal quantities are interchangeable in expressions and equations.

    • Subtraction Property of Equality: If two quantities are equal, subtracting the same value from both maintains equality.

    • Transitive Property of Equality: If one quantity equals a second, and the second equals a third, then the first quantity equals the third.

    • Zero Product Property: If the product of two factors is zero, at least one of the factors must be zero.

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    Description

    This quiz focuses on important properties and proofs in algebra. You will learn about various properties related to addition and multiplication, including the Addition Property of Equality and the Associative Property. Perfect for review and mastering algebraic concepts.

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