Numerical expressions (unlike the algebraic ones) are not meant to be left in the expression form. In other words, those are to be simplified by evaluating.

Considering the same example cited earlier, if f(x) = x + 3, then f(2) = 2 + 3 which is simplified by just adding 2 + 3 = 5.

But all algebraic expressions are not that simple and may have a number of terms connected by multiple operators. Also a term may have a parenthesis or may be a power expression or may a combination of both.

Suppose you are given a particular value of the variable and asked to evaluate the expression for that value of the variable. First task is easy. Plug in the given value for the variable wherever it appears and now the expression is a numerical expression.

But how do you proceed to evaluate, meaning simplify the numerical expression? Which operation is to be done first? We cannot always do the operations in the same order as that of order in which the expression is formed.

**For example,** if the expression is. 2 + 3 * 4 , then evaluating in the same order as 5 * 4 = 20 is highly incorrect.

Alright, then what is the method of simplification in general or what is the numerical expression solver? Mathematicians formed a rule for the order in which you have to simplify a numerical expression. That rule is famously known as ‘order of operations’. What does the rule say?

It is probable that a numerical expression may have many terms connected with all algebraic operations in between the terms. Also, a term may have a parenthesis or may be a power expression.

So, in general, the method of simplification of a numeric expression must be done in the following order.

1) Simplify the terms in all the **parentheses**.

2) Evaluate all the power expressions for the **exponents** in each power expression.

3) Do the **multiplication **and **division** that appears after the above steps. It may be noted that it is not that you have to do all the multiplications first and then do all the divisions. Both these operations have equal priority and hence, do the operation whichever comes in the order from left to right.

4) Finally complete all the **additions** and **subtractions**.

We can frame a word with all the first letters highlighted above as **PEMDAS**, which prompts us to follow the order of operations. This word also can be remembered from a humorous phrase ‘**P**lease** E**xcuse **M**e **D**ear **A**unt **S**ally’.