Mathematica Class: Proprietates de Equalitate

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Questions and Answers

What is the Addition Property of Equality?

  • If a=b, then ac=bc
  • If a=b, then a/c=b/c
  • If a=b, then a-c=b-c
  • If a=b, then a+c=b+c (correct)

What is the Subtraction Property of Equality?

  • If a=b, then a+c=b+c
  • If a=b, then a-c=b-c (correct)
  • If a=b, then a/c=b/c
  • If a=b, then ac=bc

What is the Multiplication Property of Equality?

  • If a=b, then ac=bc (correct)
  • If a=b, then a/c=b/c
  • If a=b, then a-c=b-c
  • If a=b, then a+c=b+c

What is the Division Property of Equality?

<p>If a=b, then a/c=b/c (B)</p> Signup and view all the answers

What does the Distribution Property state?

<p>if a(b=c), then a(b=c) = ab+ac (B)</p> Signup and view all the answers

What does the Substitution Property allow you to do?

<p>Replace a variable with its equal.</p> Signup and view all the answers

What does the Reflective Property state?

<p>For any real number a, a=a.</p> Signup and view all the answers

What does the Symmetric Property state?

<p>If a=b, then b=a.</p> Signup and view all the answers

What does the Transitive Property state?

<p>If a=b and b=c, then a=c.</p> Signup and view all the answers

Illustrate the idea behind the Substitution Property with an example.

<p>If m+n=15 and n=2, then m+2=15.</p> Signup and view all the answers

What is an example demonstrating the Division Property of Equality?

<p>If -7k=-42, then k=6.</p> Signup and view all the answers

Can you provide an example of the Multiplication Property of Equality?

<p>If x/4=-5, x=-20.</p> Signup and view all the answers

What is a numerical example related to the Addition Property of Equality?

<p>If c-9=-1, then c=8.</p> Signup and view all the answers

Give an example of the Transitive Property.

<p>If w2=2x and 2x=y, then w2=y.</p> Signup and view all the answers

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Study Notes

Proprietates de Equalitate

  • Addition Property of Equality: Si a=b, tunc a+c=b+c. Utilizado pro mantener equalitate durante additiones.
  • Subtraction Property of Equality: Si a=b, tunc a-c=b-c. Permitte subtractiones sin afectar la equalitate.
  • Multiplication Property of Equality: Si a=b, tunc ac=bc. Valido pro multiplicationes in systemas algebraicos.
  • Division Property of Equality: Si a=b, tunc a/c=b/c. Usato quando dividentes sunt identicalmente divided.

Proprietates Specificas

  • Distribution Property: Si a(b=c), tunc a(b+c)=ab+ac. Essential pro expansion de expressiones algebraic.
  • Reflexive Property: Omne numero real a satisface a=a. Fundamental pro identitate in mathemathica.
  • Symmetric Property: Si a=b, tunc b=a. Permitte reversion de relaciones.
  • Transitive Property: Si a=b e b=c, tunc a=c. Usado pro crear relationes indirecte.

Substitutione e Inversion

  • Substitution Property: Si a=b, tunc a pote esser subistituto per b in qualunque expression o equation. Cruciale pro simplificatione de calculationes.
  • Reflective Property: Simple affirmation que x=x, affirmando identitate.

Exemplos de Applicatio

  • Example de Distribution: 3(p-7)=3p-21. Demonstration de distributione in action.
  • Division Property of Equality: Exemplo: Si -7k=-42, tunc k=6. Clarificatione de division in contextu algebraic.
  • Substitution in Operation: Si m+n=15 e n=2, tunc m+2=15. Exemplificando substitutione in operatores.

Proprietates Repetite e Evoluzioni

  • Addition Property Example: Si c-9=-1, tunc c=8. Illustrando additione in actione.
  • Symmetric Property Example: Si n=-3, tunc -3=n, logica reversibile in actione.

Analogias e Comprensiones

  • Algebraic Context: Omnes proprietates stabilisce bases solid e logique pro manipulatione de equationes e expressiones algebraicas.
  • Fundamentale pro Studentes: Conoscere e applicare iste proprietates es essential pro successu in algebra e geometria.

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