7th Grade Section
WME@Kimpton Middle

Order of Operations

Negative IntegersWho goes first and who goes next? That is the order we are talking about here. When carrying out mathematical operations with numbers, the concept of order is important.

But before we look at the order of operations, let's first talk about operators we use for arithmetic operations.

telephone operatorAn operator is not one who works at a telephone exchange :-). In mathematics, an operator is a symbol such as + that we put between two numbers to denote an operation such as add.

+     add
&minus     subtract
× or *     multiply
÷ or /     divide
** or ^     power
( )     group together

Remember what power means? It means repeated multiplication. For example, 10^3 (10 to the power 3) means 10*10*10. Sometimes, instead of the ^ we put the power as a superscript.

103 is the same as 10 ^ 3 or 10 ** 3

  1. Now let's look at this computation and ask what it means.

    10 − 2 + 5 means (10 - 2) + 5, not 10 − (2 + 5)

    So you first subtract 2 from 10 getting 8. Then you add 8 and 5. The answer is   

  2. But what about the following?

    10 − 2 × 5

    Here you need to muitiply 2 and 5 first. So the answer is   

  3. The operator × takes precedence over the operator −. Hence the multiplication is done first. The relative precedence of operators is shown here

    PrecedenceOperator
    1(   )
    2^ or **
    3× ÷ /
    4− +

    When you have operators of the same precedence, as in 10 − 2 + 5 then the order is from left to right. Do the following problems.

    14 ÷ 2 × 3 =   
    
    14 − 2 × 3 =   
    
    -14 ÷ 2 − 3 =   
    
    14 − (-6) ÷ 2 =   
    


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