Key Equations

• • [latex]a+b=b+a[/latex] describes the commutative property of addition.
  • [latex]a \cdot b = b \cdot a[/latex] describes the commutative property of multiplication.
  • [latex]\left(a+b\right)+c=a+\left(b+c\right)[/latex] describes the associative property of addition.
  • [latex]\left(a \cdot b\right)\cdot c=a\cdot \left(b\cdot c\right)[/latex] describes the associative property of multiplication.
  • [latex]a\left(b \pm c\right)=ab \pm ac[/latex] describes the distributive property of multiplication over addition or subtraction.
  • [latex]\left(b \pm c\right)a=ba+ca[/latex] describes use of the distributive property from the right by the commutative property of multiplication.
  • [latex]a \cdot 0=0[/latex]
  • [latex]\dfrac{0}{a}=0[/latex] for all real [latex]a\neq 0[/latex]
  • [latex]\dfrac{a}{0}[/latex] is undefined for all real [latex]a[/latex].
  • [latex]a+0=a\left(0\right)+a=a[/latex] describes the identity property of addition. [latex]0[/latex] is called the additive identity.
  • [latex]a\cdot1=a\left(1\right) \cdot a=a[/latex] describes the identity property of multiplication. [latex]1[/latex] is called the multiplicative identity.
  • [latex]a+\left(-a\right)=0[/latex] describes the inverse property of addition. [latex]-a[/latex] is call the additive inverse of [latex]a[/latex].
  • [latex]a \cdot \dfrac{1}{a}=1[/latex] describes the inverse property of multiplication. [latex]\dfrac{1}{a}[/latex] is called the multiplicative inverse of [latex]a[/latex].

Glossary

irrational number

a number that cannot be written as the ratio of two integers and whose decimal form neither terminates nor repeats

real numbers

the set of real numbers includes all rational numbers and all irrational numbers

rational number

a rational number is a number that can be written in the form [latex]\dfrac{p}{q}[/latex], where [latex]p[/latex] and [latex]q[/latex] are integers and [latex]q \neq 0[/latex]