PEMDAS stands for Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction. It is a mathematical rule that is used to solve arithmetic problems effectively.
The order of operations is the rules that tell 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).
In this article, we will learn about the PEMDAS Rule with its order of operations, its applications, examples, and others in detail.
Table of Content
What is PEMDAS Rule?
PEMDAS is a useful method for remembering the sequence in which you should answer maths problems. It represents parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
So, when you have a math problem with multiple operations such as addition, subtraction, multiplication, and division, PEMDAS instructs you to begin with parentheses, then exponents, then multiplication and division (whichever comes first from left to right), and finally addition and subtraction. It’s like a guide for solving maths riddles! 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
= 7 × 2
= 14
Student B solved is as: 11 – 2 × 2
= 11 – 4
= 7
Both students solved correctly according to their understanding but only one is correct we will learn the correct way of solving such expression is explained using PEMDAS in this article.
PEMDAS Definition
PEMDAS is a math acronym that stands for
- Parentheses
- Exponents
- Multiplication and Division
- Addition and Subtraction
It denotes the sequence of operations in solving mathematical formulas. Parentheses are computed first, then exponents. Then, multiply and divide from left to right, followed by addition and subtraction. PEMDAS guarantees correct answers by prioritising the order of operations in equations.
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 little integers that inform us how many times we can multiply a given number. These computations are performed after the brackets.
- MD stands for Multiplication and Division, performed in the left-to-right direction.
- AS stands for Addition and Subtraction, performed in the left to right direction.
Using PEMDAS rule one will always get the right answer.
PEMDAS Rule
PEMDAS is a set of recommendations 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.
|
P |
[{( )}] |
Parentheses |
|---|---|---|
|
E |
x2 |
Exponents |
|
M or D |
x or ÷ |
Multiplication or Division |
|
Aor S |
+ or – |
Addition or Subtraction |
PEMDAS rule full form can be learnt by the image added below:
PEMDAS Rule
Using the PEMDAS sequence guarantees exact solutions. A simple mnemonic for PEMDAS is “Please Excuse My Dear Aunt Sally.”
PEMDAS Rule Examples
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.
PEMDAS Rule – Order of Operations
In the field of mathematical operations, an organised sequence must be followed: parentheses, exponents, multiplication, division, addition, and subtraction, sometimes known as PEMDAS.
- Parentheses: When encountered, prioritise operations within them. This may necessitate further dissection based on the overall order of procedures. Nested brackets necessitate an inside-out approach.
- Exponents: Next, handle any exponents that appear in the equation.
- Multiplication and Division: These operations are interconnected, providing for flexibility in their execution sequence. Nonetheless, they must come after brackets and exponents, but before addition and subtraction.
- Addition and Subtraction: These two processes, albeit separate, work together in the same step. It makes no difference whether you start with addition or subtraction. However, they appear only after brackets, exponents, and any previous multiplication or division.
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 programme 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
|
PEMDAS |
BODMAS |
|---|---|
|
Used for the systematic simplification of mathematical operations such as division, multiplication, addition, and subtraction. |
It is also used to simplify arithmetic operations like division, multiplication, addition, and subtraction in an orderly fashion. |
|
|
Important Points on PEMDAS Rule
- Always prioritize actions enclosed in parentheses, resolving them before everything else.
- Proceed with any exponents in the next step.
- When dealing with multiplication or division, work from left to right, starting with the operation that occurs first.
- Finally, solve addition and subtraction in a left-to-right order, with the first operation taking priority.
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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 – 12}]
=> [18 + {12 – 12}]
=> [18 + 0]
=> 18
Example 2: Calculate: (14 + 2/ 3 + 1) – 2
Solution:
Step 1: (14 + 2/ 3 + 1) – 2
Step 2: (16 / 4) – 2
Step 3: 4 – 2
Step 4: 2
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
Practice Problems on PEMDAS Rule
P1: Solve 2 – 7 ÷ (6 – 2) × 3 + 8 using PEMDAS.
P2: Solve: 5 + 8 × (2 + 3) ÷ 4 – 3 using PEMDAS.
P3: Simplify the expression with the PEMDAS rule: 15 ÷ (6 – 3 × 4).
P4: Calculate: [20 + {12 – (5 x 8)}]
Summary – PEMDAS Rule (Order of Operations)
The PEMDAS rule is a handy guide used to solve math problems involving more than one operation, such as addition, subtraction, multiplication, and division. It stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This rule tells you the order to tackle different parts of a math problem: start with any calculations inside parentheses, then move on to exponents. After that, handle any multiplication or division as they appear from left to right, and finally, do the same with addition and subtraction. This method ensures you solve math equations correctly, avoiding mix-ups that can happen if you don’t follow the correct order of operations. Whether you’re working on engineering problems, computer science algorithms, or just doing your math homework, using PEMDAS helps you get the right answer every time.
FAQs on PEMDAS Rule
What is PEMDAS, and why is it relevant in mathematics?
PEMDAS is an abbreviation for parentheses, exponents, multiplication and division (from left to right), and addition and subtraction. It is critical because it offers a methodical technique to solving mathematical problems, resulting in precise solutions.
How does PEMDAS assist solve hard mathematical problems?
PEMDAS specifies the sequence in which operations should be executed, reducing confusion and providing consistency when solving expressions comprising several operations.
How is PEMDAS different from BODMAS?
While PEMDAS and BODMAS have the same goal of directing the sequence of operations, their nomenclature differs. PEMDAS employs brackets, whereas BODMAS uses brackets; similarly, PEMDAS refers to exponents, whilst BODMAS refers to orders.
What mnemonic techniques may be used to memorize the PEMDAS order of operations?
Mnemonic strategies like as “Please Excuse My Dear Aunt Sally” help recall the order of brackets, exponents, multiplication and division, addition, and subtraction.
Can you demonstrate how to use PEMDAS with an example?
Certainly! Consider this expression: 5 + 2[10 – 3(4 – 2)] ÷ 2. We’d start by figuring out what’s behind the brackets, then handle exponents, multiplication/division, and lastly addition/subtraction.
What are some frequent blunders made when using PEMDAS?
One typical issue is forgetting to address operations within brackets first, or failing to recognise the importance of exponents, which leads to inaccuracies in the final answer.
How can one become proficient in applying PEMDAS to mathematical problem solving?
Practicing a range of mathematical problems and returning to the concept of PEMDAS on a frequent basis strengthens knowledge and competency in its application, eventually improving problem-solving abilities.