Mathematics » The Language of Algebra » Use the Language of Algebra

Summary and Key Concepts

Key Concepts

OperationNotationSay: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
    • \(a<b\) is read \(a\) is less than \(b\)
    • \(a\) 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
       

      ..

Algebraic NotationSay
\(a=b\)\(a\) is equal to \(b\)
\(a\ne b\)\(a\) is not equal to \(b\)
\(a<b\)\(a\) 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.


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