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Glossary of terms

E

  • Title

    Equation

  • Description

    An equation is a mathematical sentence. It is a way of showing that one expression is equal to another expression.

    An equation should be thought of as a balance. The two sides of the equation must always be equal, so when we are manipulating equations, it is essential that we perform the same (allowable) operations to both sides of the equals sign.

  • Example of use

    Here are 2 equations. Note that there is always an expression either side of an equals sign.

    $2x+3=11$

    $x^2 - x -6=0$

  • See also

  • Title

    Exponent

  • Description

    An exponent is another name for a power or index. In the expression $x^3$, the $3$ is the exponent, index, power or order of the expression.

    Exponents are a shorthand for repeated multiplication, in much the same way as multiplication is a shorthand for repeated addition.

  • Example of use

    $p \times p \times p \times p \times p = p^5$

    In the expression, $r^{-3}$, the exponent of $r$ is $-3$.

  • See also

  • Title

    Expression

  • Description

    An expression is the mathematical equivalent of a phrase or clause in standard language. It is not usually a complete sentence unless it is part of an equation or inequality. The simplest expression would be a term, which can be a number ($3$) or letter representing a number ($x$), or a combination of the two like  $2x$.

    More complex expressions, like $2x^3 - 3x^2 + 4x -5$ can be made up from several terms connected with operators ($+ - \times \div$).

  • Example of use

    Q: If an apple costs  $t$  pence, how much do 20 apples cost?

    A: $20t$  pence.

    Q: Simplify  $x +2x +4x$

    A: $7x$

  • See also