Key Concepts
| Operation | Notation | Say: | The result is… |
|---|---|---|---|
| Addition | [latex]a+b[/latex] | [latex]a[/latex] plus [latex]b[/latex] | the sum of [latex]a[/latex] and [latex]b[/latex] |
| Multiplication | [latex]a\cdot b,\left(a\right)\left(b\right),\left(a\right)b,a\left(b\right)[/latex] | [latex]a[/latex] times [latex]b[/latex] | the product of [latex]a[/latex] and [latex]b[/latex] |
| Subtraction | [latex]a-b[/latex] | [latex]a[/latex] minus [latex]b[/latex] | the difference of [latex]a[/latex] and [latex]b[/latex] |
| Division | [latex]a\div b,a/b,\frac{a}{b},b\overline{)a}[/latex] | [latex]a[/latex] divided by [latex]b[/latex] | the quotient of [latex]a[/latex] and [latex]b[/latex] |
- Equality Symbol
- [latex]a=b[/latex] is read as [latex]a[/latex] is equal to [latex]b[/latex]
- The symbol [latex]=[/latex] is called the equal sign.
- Inequality
- [latex]a<b[/latex] is read [latex]a[/latex] is less than [latex]b[/latex]
- [latex]a[/latex] is to the left of [latex]b[/latex] on the number line
- [latex]a>b[/latex] is read [latex]a[/latex] is greater than [latex]b[/latex]
- [latex]a[/latex] is to the right of [latex]b[/latex] on the number line
| Algebraic Notation | Say |
|---|---|
| [latex]a=b[/latex] | [latex]a[/latex] is equal to [latex]b[/latex] |
| [latex]a\ne b[/latex] | [latex]a[/latex] is not equal to [latex]b[/latex] |
| [latex]a<b[/latex] | [latex]a[/latex] is less than [latex]b[/latex] |
| [latex]a>b[/latex] | [latex]a[/latex] is greater than [latex]b[/latex] |
| [latex]a\le b[/latex] | [latex]a[/latex] is less than or equal to [latex]b[/latex] |
| [latex]a\ge b[/latex] | [latex]a[/latex] is greater than or equal to [latex]b[/latex] |
- Exponential Notation
- For any expression [latex]{a}^{n}[/latex] is a factor multiplied by itself [latex]n[/latex] times, if [latex]n[/latex] is a positive integer.
- [latex]{a}^{n}[/latex] means multiply [latex]n[/latex] factors of [latex]a[/latex]
- The expression of [latex]{a}^{n}[/latex] is read [latex]a[/latex] to the [latex]n[/latex]th power.
Order of Operations When simplifying mathematical expressions perform the operations in the following order:
- Parentheses and other Grouping Symbols: Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.
- Exponents: Simplify all expressions with exponents.
- Multiplication and Division: Perform all multiplication and division in order from left to right. These operations have equal priority.
- Addition and Subtraction: Perform all addition and subtraction in order from left to right. These operations have equal priority.
Glossary
- expressions
- An expression is a number, a variable, or a combination of numbers and variables and operation symbols.
- equation
- An equation is made up of two expressions connected by an equal sign.
