# Order of Operations

Concept

**Order of Operations** is the standard method in evaluating arithmetic expressions. Without the order of operations, students may obtain different answers to the same expression, depending on the student's preference in order in evaluating

Problem:

Evaluate the arithmetic expression 3 + 5 x 3.

Student A |
Student B |

3 + 5 x 3
= 3 + 15 |
3 + 5 x 3
= 8 x 3 |

= 18 |
= 24 |

As we can clearly see, both students got different answers to the same problem. Student A decided to multiply first before doing the addition whereas student B did the exact opposite. This is unacceptable as there can only be one correct answer in the evaluation of arithmetic expressions.

That is why mathematicians have come together to agreed on a set of rules to avoid confusion.

Basically, the order of operations tells of the order, in which the student should first approach operations such as parentheses, division, multiplication, subtraction and addition.

## Rules to follow when using the Order of Operations.

1. First, evaluate the operations within the parentheses.

2. Next, reduce the exponents and roots to its numerical form.

3. Afterwards, do all the multiplication and division from the left to right.

4. Finally, do the addition and subtraction to obtain the final answer.

Example

Let us look at how order of operation works.

3 x 16 – ( 4 +3 x 5)

According to the order of operations, we work out everything within the parentheses. In following rules (3) and (4) within the brackets, we have to multiply first before adding.

Now that the brackets have been removed, we can proceed on with the rest of the operations.

3 x – 19

Next, we find the value of
.

3 x 4 - 19

Then, we multiply the terms and finally subtract to obtain the final answer of – 7.

Scholar's tips: Order of operations offer flexibility in writing mathematical expressions. Since addition and multiplication are commutative, it follows that 3 x 4 +2 can be written as 4 x 3 + 2 , 2 + 3 x 4 , 2 + 4 x 3 . It doesn't change the mathematical concept behind the expression.

'Try it Yourself' Section

Try applying the order of operations yourself with the following problems.

a) 3 x 2- (3+2)/5

b) [(15 -2) x ] /4

You can try some of our interesting interactive games for learning the order of operations. They are fun and are bound to stimulate your interest in learning order of operations.

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