Key Concepts
- Identity Properties
- Identity Property of Addition:
For any real number [latex]a[/latex]: [latex]a+0=a(0)+a=a[/latex]. [latex]0[/latex] is the additive identity - Identity Property of Multiplication:
For any real number [latex]a[/latex]:- [latex]a\cdot 1=a[/latex]
- [latex]1\cdot a=a[/latex]
- [latex]1[/latex] is the multiplicative identity
- Identity Property of Addition:
- Inverse Properties
- Inverse Property of Addition: For any real number [latex]a[/latex]: [latex]a+\left(-a\right)=0-a[/latex] is the additive inverse of [latex]a[/latex]
- Inverse Property of Multiplication: For any real number [latex]a[/latex]: [latex]\left(a\ne 0\right)a\cdot {\Large\frac{1}{a}}=1[/latex]. The multiplicative inverse of [latex]a[/latex] is [latex]{\Large\frac{1}{a}}[/latex].
- Properties of Zero
- Multiplication by Zero: For any real number [latex]a[/latex],
[latex]\begin{array}{ccccccc}\hfill a\cdot 0=0\hfill & & & \hfill 0\cdot a=0\hfill & & & \hfill \text{The product of any number and 0 is 0.}\hfill \end{array}[/latex] - Division of Zero: For any real number [latex]a[/latex],
[latex]\begin{array}{ccccccc}\hfill {\Large\frac{0}{a}}=0\hfill & & & \hfill 0+a=0\hfill & & & \hfill \text{Zero divided by any real number, except itself, is zero.}\hfill \end{array}[/latex] - Division by Zero: For any real number [latex]a[/latex], [latex]{\Large\frac{0}{a}}[/latex] is undefined and [latex]a\div 0[/latex] is undefined. Division by zero is undefined.
- Multiplication by Zero: For any real number [latex]a[/latex],
Glossary
- Additive Identity
- The additive identity is [latex]0[/latex]. When zero is added to any number, it does not change the value.
- Additive Inverse
- The opposite of a number is its additive inverse. The additive inverse of a is [latex]-a[/latex] .
- Multiplicative Identity
- The multiplicative identity is [latex]1[/latex]. When one multiplies any number, it does not change the value.
- Multiplicative Inverse
- The reciprocal of a number is its multiplicative inverse. The multiplicative inverse of [latex]a[/latex] is [latex]{\Large\frac{1}{a}}[/latex] .
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