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Algebraic Properties (5th Grade)

Properties essential for expanding our knowledge of number sense and relationships in equations.
a data set by pmerrill
created November 15, 2016
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FAMILY TREE
NameAddition EquationMultiplication EquationDescription
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.
Commutativea+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.
Identitya+0=a=0+aax1=a=1xaIn addition, any number plus 0, or 0 plus any number will equal that number. In multiplication, any number times one will equal itself.
Inversea+(-a)=0=(-a)+aaX1/a=1=1/aXaIn 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.
Distributivea(bc)=ab+aca(bc)=ab+acWe 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.
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