Order of Operations

The order of operations is a set of rules used to determine the sequence in which mathematical operations should be performed in an equation.

It is important to follow these rules to ensure that the calculations are performed correctly and consistently. Failure to follow the order of operations can result in incorrect solutions to mathematical problems.

The Order of Operations

The order of operations is commonly remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Parentheses: Perform operations inside parentheses first. If there are nested parentheses, start with the innermost set of parentheses and work outward.

Exponents: Perform any calculations involving exponents or powers.

Multiplication and Division: Perform multiplication and division in order from left to right.

Addition and Subtraction: Perform addition and subtraction in order from left to right.

Example:

Let’s take the following expression: 6 ÷ 2(1 + 2)

To solve this equation using the order of operations, we would follow the steps as follows:

Start with the parentheses: 1 + 2 = 3
Next, perform multiplication and division in order from left to right: 6 ÷ 2(3)
Now, we have to use PEMDAS again since we have multiplication and division at the same level: 2(3) = 6
Finally, perform the division: 6 ÷ 6 = 1
So the solution to the equation is 1.

Practice Exercise

Now that you have learned about the order of operations in mathematics, let’s try a practice exercise.

2 + 3 × 4
(5 + 2) × 3
10 − 2 × 3²
6 ÷ 2 + 1

Answers:

14
21
4
4

The order of operations is essential in mathematics to ensure that calculations are performed correctly and consistently.

By following the rules of PEMDAS, you can solve mathematical problems with ease. Remember to always perform operations inside parentheses first, then work from left to right when performing multiplication, division, addition, and subtraction.