# Algebraic Properties (5th Grade)

Properties essential for expanding our knowledge of number sense and relationships in equations.

Play a game to test your knowledge!

One of these names is not like the others....

Find Which name does not belong in the sort! Explore algebraic properties to help master key concepts you will use throughout high school!

What fits?

Match the name of a property to its addition equation, multiplication equation and it's description!

Associate the Associative Property (and others!)

Match the Property Name to either its description, multiplication or addition card!

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Name | Addition Equation | Multiplication Equation | Description |
---|---|---|---|

Associative | (a+b)+c=a+(b+c) | (ab)c=a(bc) | In addition and multiplication, it doesn't matter in which way we group the numbers using parenthesis. If the same numbers and same amount of those numbers are used, we will get the same number. |

Commutative | a+b=b+a | (ab)=(ba) | In addition and multiplication, it does not matter in which order we add or multiply the numbers. If the same numbers and same amount of numbers are used, we will get the same number. |

Identity | a+0=a=0+a | ax1=a=1xa | In addition, any number plus 0, or 0 plus any number will equal that number. In multiplication, any number times one will equal itself. |

Inverse | a+(-a)=0=(-a)+a | aX1/a=1=1/aXa | In addition any number added to it's inverse (or itself, negative) will equal 0. In multiplication, any number multiplied by one over itself will equal 1, so long as that number is not 0. |

Distributive | a(bc)=ab+ac | a(bc)=ab+ac | We need to use both addition and multiplication to understand this property. Any two numbers multiplied together before being multiplied by another number can be seperately multiplied and then added to get the same answer. |