What is PEMDAS?

S3-SA1-0086

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

PEMDAS is a special order we follow when solving math problems that have different types of operations like addition, subtraction, multiplication, and division. It helps make sure everyone gets the same correct answer for the same problem. Think of it as traffic rules for math calculations.

Simple Example

Quick Example

Imagine you bought 3 samosas for Rs 10 each and 2 cold drinks for Rs 20 each. If you just add all numbers from left to right, you might get the wrong total. PEMDAS tells you to first calculate the cost of samosas (3 x 10 = 30) and cold drinks (2 x 20 = 40) separately, and then add those totals (30 + 40 = 70) to find your total bill of Rs 70. This ensures you calculate costs correctly.

Worked Example

Step-by-Step

Let's solve: 10 + 4 x (6 - 2) / 2

1. P (Parentheses): First, solve what's inside the brackets.
6 - 2 = 4
Now the problem is: 10 + 4 x 4 / 2
---2. E (Exponents): There are no exponents in this problem, so we skip this step.
---3. MD (Multiplication and Division) from left to right: Next, do multiplication or division as you encounter them from left to right.
4 x 4 = 16
Now the problem is: 10 + 16 / 2
---4. MD (Multiplication and Division) from left to right: Continue with division.
16 / 2 = 8
Now the problem is: 10 + 8
---5. AS (Addition and Subtraction) from left to right: Finally, do addition or subtraction as you encounter them from left to right.
10 + 8 = 18

Answer: 18

Why It Matters

PEMDAS is super important because it ensures everyone gets the same answer to a math problem, which is crucial in fields like Computer Science and Engineering. When building apps or designing bridges, precise calculations are a must. Data scientists use it to correctly analyze vast amounts of information, and even economists rely on it for financial modeling.

Common Mistakes

MISTAKE: Always doing multiplication before division, or addition before subtraction, even if division or subtraction comes first from the left. | CORRECTION: Remember that Multiplication and Division have equal priority, and you solve them from left to right. The same applies to Addition and Subtraction.

MISTAKE: Forgetting to solve operations inside parentheses first. | CORRECTION: Always start with operations inside parentheses (brackets) before anything else, as 'P' in PEMDAS stands for Parentheses.

MISTAKE: Confusing the order of operations when exponents are present. | CORRECTION: After Parentheses, the next step is Exponents. Make sure to calculate any powers or roots before moving to multiplication or division.

Practice Questions

Try It Yourself

QUESTION: Solve: 5 + 3 x 2 | ANSWER: 11

QUESTION: Solve: 12 / (2 + 4) - 1 | ANSWER: 1

QUESTION: A class has 20 students. 3 groups of 4 students each are working on a project. How many students are NOT in these groups? (Solve using PEMDAS principles) | ANSWER: 8

MCQ

Quick Quiz

What is the correct answer for 18 - 6 / 3 + 2?

The Correct Answer Is:

According to PEMDAS, division comes before subtraction and addition. So, first calculate 6 / 3 = 2. Then, solve from left to right: 18 - 2 + 2 = 16 + 2 = 18. Therefore, option B is correct.

Real World Connection

In the Real World

Imagine you're calculating your monthly mobile data usage. If you use 2 GB daily for 10 days and then buy an extra 5 GB pack, PEMDAS helps you correctly calculate your total usage: (2 x 10) + 5 = 25 GB. Similarly, when engineers at ISRO calculate rocket trajectories, or when a stock market analyst predicts share prices, they use PEMDAS-like rules to ensure their complex equations are solved accurately.

Key Vocabulary

Key Terms

OPERATION: A mathematical action like addition, subtraction, multiplication, or division. | PARENTHESES: Brackets () used to group parts of an expression. | EXPONENTS: A number indicating how many times a base number is multiplied by itself (e.g., 2 in 5^2). | PRIORITY: The order in which operations should be performed.

What's Next

What to Learn Next

Great job understanding PEMDAS! Now that you know the order of operations, you're ready to tackle more complex algebraic expressions. Next, you can learn about 'Integers' and 'Algebraic Expressions' which often use these rules to solve problems with variables.