Summary and Key Concepts
Key Concepts
| Operation | Notation | Say: | The result is… |
|---|---|---|---|
| Addition | \(a+b\) | \(a\phantom{\rule{0.2em}{0ex}}\text{plus}\phantom{\rule{0.2em}{0ex}}b\) | the sum of \(a\) and \(b\) |
| Multiplication | \(a·b,\left(a\right)\left(b\right),\left(a\right)b,a\left(b\right)\) | \(a\phantom{\rule{0.2em}{0ex}}\text{times}\phantom{\rule{0.2em}{0ex}}b\) | The product of \(a\) and \(b\) |
| Subtraction | \(a-b\) | \(a\phantom{\rule{0.2em}{0ex}}\text{minus}\phantom{\rule{0.2em}{0ex}}b\) | the difference of \(a\) and \(b\) |
| Division | \(a÷b,a/b,\phantom{\rule{0.2em}{0ex}}\frac{a}{b},b\overline{)a}\) | \(a\) divided by \(b\) | The quotient of \(a\) and \(b\) |
- Equality Symbol
- \(a=b\) is read as \(a\) is equal to \(b\)
- The symbol \(=\) is called the equal sign.
- Inequality
- \(a
- \(a\) is to the left of \(b\) on the number line
- \(a>b\) is read \(a\) is greater than \(b\)
- \(a\) is to the right of \(b\) on the number line
- \(a
| Algebraic Notation | Say |
|---|---|
| \(a=b\) | \(a\) is equal to \(b\) |
| \(a\ne b\) | \(a\) is not equal to \(b\) |
| \(a |
\(a\) is less than \(b\) |
| \(a>b\) | \(a\) is greater than \(b\) |
| \(a\le b\) | \(a\) is less than or equal to \(b\) |
| \(a\ge b\) | \(a\) is greater than or equal to \(b\) |
- Exponential Notation
- For any expression \({a}^{n}\) is a factor multiplied by itself \(n\) times, if \(n\) is a positive integer.
- \({a}^{n}\) means multiply \(n\) factors of \(a\)
- The expression of \({a}^{n}\) is read \(a\) to the \(n\text{th}\) 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.
This lesson is part of:
The Language of Algebra
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