PEMDAS Rule | Order of Operations

PEMDAS is an acronym for a mathematical rule that defines the order to solve arithmetic problems effectively.

The PEMDAS rule tells us the sequence in which the expression with multiple operations is solved. The order is PEMDAS: Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction (from left to right).

PEMDAS Full Form

PEMDAS is a collection of rules in mathematics that help us solve problems in the correct sequence. It's similar to a recipe for solving arithmetic problems.

• P stands for Parentheses, which are essentially containers that house numbers and operations. First, we deal with what is inside them.
• E stands for Exponents, which are integers that inform us how many times we can multiply a given number.
• M stands for Multiplication
• D stands for Division,
• AS stands for Addition and Subtraction, performed from left to right direction.

Using the PEMDAS rule, one will always get the right answer.

PEMDAS Rule- Order of Operations

PEMDAS is a set of recommendations that define the order of operations for solving mathematical equations properly.

• It begins with brackets, which prioritize the processes encompassed inside them.
• Following that, exponents and powers are discussed.
• Then, multiplication and division are done from left to right.
• Finally, addition and subtraction are done the same way.

Solving Problems with the PEMDAS Rule

When you have a math problem with multiple operations such as addition, subtraction, multiplication, and division, the PEMDAS rule helps you to perform the operations in a correct order, it instructs you to begin with parentheses, then exponents, then multiplication and division (whichever comes first from left to right), and finally addition and subtraction.

Note: PEMDAS or PEDMAS is same as BODMAS both rules correctly define the order of operation to solve a mathematical operation.

The use of PEMDAS is explained using the example below:

Suppose in a class, two students A and B are asked to solve 11 - 2 × 2

Student A solved it as 11 - 2 × 2 (Incorrect way)

= 9 × 2
= 18

Student B solved it as: 11 - 2 × 2 (Correct way)

= 11 - 4
= 7

Both students solved correctly according to their understanding but only the second one is correct as it is done in the correct order. We will learn the correct way of solving such expressions is explained using PEMDAS in this article.

PEMDAS Rule Solved Example

Let us explain PEMDAS with an example.

5 + 2[10 - 3(4 - 2)] ÷ 2

We will begin by working from the inside of the brackets. We will begin by solving the innermost bracket and then proceed to the outermost bracket.

Step 1: Solve for 4 - 2, which equals 2. The equation becomes 5 + 2[10 - 3(2)] ÷ 2.

Step 2: Compute 3(2), which equals 6. The equation becomes 5 + 2[10 - 6] ÷ 2.

Step 3: Now, between the parentheses, answer 10 - 6 = 4. Our equation is now 5 + 2[4] ÷2.

Step 4: Then, address what's between the brackets 2[4] = 8. Our expression now looks like 5 + 8 ÷ 2.

Step 5: Following PEMDAS, we divide first 8 ÷ 2 = 4. The equation becomes 5 + 4.

Step 6: Finally, add 5 and 4, and we have our final answer: 9.

By using PEMDAS, you may effortlessly solve hard arithmetic problems and thrive in your math career.

Applications of PEMDAS Rule

Understanding the sequence of operations in mathematics is essential for many fields and daily situations. Let's look at some significant uses of PEMDAS in various sectors and how they help to ensure precision and dependability.

• Engineering: When designing structures such as bridges, engineers utilize PEMDAS to properly calculate loads and stresses, assuring the structure's safety and stability.
• Computer Science: PEMDAS helps verify that algorithms provide proper results while coding. For example, in a program that calculates distances between points on a map, the sequence of operations guarantees that the results are accurate.
• Economics and Finance: Financial analysts utilize PEMDAS to calculate financial indicators like net present value and internal rate of return, which are critical for making sound investment decisions.
• Pharmacists: Pharmacists use PEMDAS to precisely determine medicine doses. Using the exact order of procedures is crucial to avoid giving patients wrong dosages of medication, which might be dangerous.
• Architecture and Construction: When planning structures, architects utilize PEMDAS to compute dimensions, angles, and structural integrity. Following the proper sequence of procedures ensures that structures are both visually beautiful and structurally stable.

PEMDAS Rule vs BODMAS Rule

The following table compares PEMDAS with BODMAS

People Also Read:

• Solve Simplifications Using BODMAS Rules
• BODMAS Rule in Math

PEMDAS Rule Solved Examples

Example 1: Simplify the equation with the PEMDAS rule: [18 + {12 – (4 x 8)}]
Solution:

=> [18 + {12 – (4 x 8)}]
= [18 + {12 – 32}]
=> [18 + {-20}]
=> [18 - 20]
=> -2

Example 2: Calculate: 3 × 3 - 3 ÷ 3 + 3.
Solution:

=> 3 × 3 - 3 ÷ 3 + 3
=> 9 - 3 ÷ 3 + 3
=> 9 - 1 + 3
=> 9 + 2
=> 11

Example 3: Solve: 5 + 8 × (3 + 8) ÷ 4 – 6 using PEMDAS.
Solution:

Step 1 (Parentheses): 5 + 8 × (3 + 8) ÷ 4 – 6 = 5 + 8 × 11 ÷ 4 – 6
Step 2 (Multiplication): 5 + 8 × 11 ÷ 4 – 6 = 5 + 88 ÷ 4 – 6
Step 3 (Division): 5 + 88 ÷ 4 – 6 = 5 + 22 – 6
Step 4 (Addition): 5 + 22 – 6 = 27 - 6
Step 5 (Subtraction): 27 - 6 = 21