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Fundamental Laws of Algebra (Economics)

Fundamental Laws of Algebra

The Fundamental Laws of Algebra are rules which we must follow when performing operations with numbers or variables.

Commutative Law

The commutative law says that the order in which we add or multiply two (or more) numbers doesn't matter: \[a+b=b+a\] \[a\times b=b\times a\]

Examples:
  • $5+10=10+5=15$
  • $1+2+3=2+1+3=3+2+1=6$
  • $5\times10=10\times5=50$
  • $1\times2\times3=2\times1\times3=3\times2\times1=6$

Associative Law of Addition

The associative law says that when you add or multiply several numbers, the grouping (or association) of the numbers doesn't affect the result: \[(a+b)+c=a+(b+c)\] \[ab(c)=a(bc)\]

Examples:
  • $(7+5)+2=7+(5+2)=14$
  • $(1+2+4)+5=(1+2)+(4+5)=12$
  • $(5\times2)\times10=5\times(2\times10)=100$
  • $(2\times3)\times(4\times1)=(2\times3\times4)\times1=24$

Distributive Law

The distributive law says that we get the same result whether we multiplying a number by a group of numbers added together or do each multiplication separately:

\[a(b+c)=ab+ac\] \[(a+b)c=ac+bc\]

Examples:
  • $5(4+2)=5\times4+5\times2=30$
  • $1(3+10)=1\times3+1\times10=13$

External Resources

Whiteboard maths

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