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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Real numbers have certain properties when it comes to operations, identities, and equalities.

When performing operations on real numbers five different properties can be used.

Name | Property |
---|---|

Distributive Property | $a⋅(a+c)=a⋅b+a⋅c$ |

Commutative Property of Addition | $a+b=b+a$ |

Commutative Property of Multiplication | $a⋅b=b⋅a$ |

Associative Property of Addition | $(a+b)+c=a+(b+c)$ |

Associative Property of Multiplication | $(a⋅b)⋅c=a⋅(b⋅c)$ |

These properties can be used when solving equations or simplifying expressions to easier find the correct solution.

Real numbers have two important identities (equations that always hold true).

Additive Identity | $a+0=0$ |

Multiplicative Identity | $a⋅1=a$ |

The equalities for real numbers indicates that different operations can be performed on equations and still yield the same equation.

Name | Property |
---|---|

Addition Property of Equality | If $a=b,$ then $a+c=b+c$ |

Subtraction Property of Equality | If $a=b,$ then $a−c=b−c$ |

Multiplication Property of Equality | If $a=b,$ then $a⋅c=b⋅c$ |

Division Property of Equality | If $a=b,$ then $ca =cb $ |

Finally, there are two special equalities; *Symmetric Property of Equality* and *Transitive Property of Equality.*

Real numbers can be written in different ways. For example $0.75=43 $ and $2.5=221 .$ The *Symmetric Property of Equality* then implies that the order does not matter.
$0.75=43 2.5=221 ⇔43 =0.75⇔2.5 $

Given three real numbers, $a,b,$ and $c,$ the transitive property of equality refers to:

If $a=b$ and $b=c,$ then $a=c.$

Real numbers are said to be closed under addition and multiplication. That is, adding or multiplying two real numbers results in a real number.