How To Write Algebraic Expressions

In mathematics, algebra is where we use letters or symbols to represent unknown numbers

Variable: A variable is a symbol, usually a letter used to represent a number. Any letter may be used as a variable.

We use algebra to translate words into mathematics. For example suppose we use the variable n to represent any unknown number we do not know in the following sentences.

        1) a number plus 3 becomes                                         n + 3
        2) four times a number becomes                                 4n
        3) three less than a number becomes                         n-3
        4) eight more than a number becomes                      8 + n
        5) Sally is four times as old as James less three years
            In the above problem we let                                    n=James’s age so
                                                                                                 4n-3=Sally’s age

To write multiplication using variables always put the multiplier (number) before the variable.

          Example: 4n   correctly means 4 times n
                          n4   incorrect
Another acceptable method of writing multiplication is to use parentheses.
          Example: 4(n) – correctly means 4 times n – notice there is no symbol between the number and the parentheses

To write division using variables we rarely use the ¸ symbol, we usually use the fraction bar.
            Example: 8¸n or   is correctly written

An expression is a group of symbols that does not contain an equal sign. Because it has no equal sign, it cannot be solved.
          Example: 4 + b
We cannot solve the expression listed above because we do not know what b represents.

An equation is an expression or group of expressions that has an equal sign. An equation can be solved.
         Example: 4 + b = 10
We can solve this because we know that b must equal 6.