Key Equations
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- [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]