Why is the order of operations important?

The order of operations is a group of rules that tells you the right order in which to solve different parts of a math problem. It is like an agreement we all made to be sure that we read and understand a problem the same way.

According to the order of operations, we need to first solve the equations in brackets and parentheses. Since they come as packages brackets and parentheses need to be solved independently. In other words, you need to solve the operations in the parentheses following the order of operations. The parentheses show you where to start. Next, come the exponents which also come as a package and have to be simplified first. Then comes multiplication and division and last addition and subtraction. It is important to make sure that we do multiplication, division, addition, and subtraction from left to right.

Students often wonder why we need to follow the order of operations. A way to help them understand is to play a little game with them. Give a number problem with mixed operations, for example 4+ 20 x 3 – 2= and ask all students to solve in any order they want. There will be many answers for the same problem. So which one is correct? It is very confusing. That’s why we need this special rule called “order of operations”

A number sentence or mathematical sentence may represent a word problem. Therefore it needs to be solved in a way that makes sense for the problem.

For example, what is the number sentence for the following problem?

A farmer sells his apples at the market for $3 per Kg and his oranges for $5 per Kg. He pays $10 per day to rent the table at the farmer’s market. On Monday he sold 12Kg of apples and 9 Kg of oranges. How much money did he make on Monday?

The correct number sentence is [(3×12)+(5×9)]-10=

If I ignore the order of operations and I do the addition first I will be adding 12+5, 12 is the number of kilograms and 5 is 5 dollars. It doesn’t make any sense to add them together.

Examples like this will show the students that the order of operation is very important.

Some more examples

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