What is the Order of Operations? | Simple Explanation for Class 6

S3-SA4-0403

What is the Order of Operations (Number Theory)?

Grade Level:

Class 6

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

Definition

What is it?

The Order of Operations is a set of rules that tells us the correct sequence to solve mathematical problems with multiple operations (like addition, subtraction, multiplication, and division). It ensures that everyone gets the same answer for the same problem, no matter who solves it. Think of it as traffic rules for math calculations!

Simple Example

Quick Example

Imagine you go to a shop and buy 2 packets of biscuits at Rs 10 each and 1 chocolate for Rs 5. If you calculate 2 + 10 x 5, you might get 12 x 5 = 60 (wrong!). But if you follow the order of operations, you do 10 x 2 first (Rs 20 for biscuits) and then add 5 (Rs 5 for chocolate), getting Rs 25. This is the correct total.

Worked Example

Step-by-Step

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

Step 1: Solve operations inside Parentheses first.
(6 - 2) = 4
So, the problem becomes: 10 + 4 x 4 / 2
---
Step 2: Next, solve Multiplication and Division from left to right.
First, 4 x 4 = 16
So, the problem becomes: 10 + 16 / 2
---
Step 3: Continue with Multiplication and Division from left to right.
Next, 16 / 2 = 8
So, the problem becomes: 10 + 8
---
Step 4: Finally, solve Addition and Subtraction from left to right.
10 + 8 = 18

Answer: 18

Why It Matters

Understanding the order of operations is crucial for building accurate computer programs and analyzing data in fields like AI/ML and Data Science. Engineers use it to design safe structures, and economists use it to calculate financial models. It's a foundational skill for many exciting careers!

Common Mistakes

MISTAKE: Solving addition before multiplication or division. For example, in 5 + 2 x 3, students might do 5 + 2 = 7, then 7 x 3 = 21. | CORRECTION: Always perform multiplication and division before addition and subtraction. In 5 + 2 x 3, first do 2 x 3 = 6, then 5 + 6 = 11.

MISTAKE: Solving operations from left to right without considering the hierarchy (like doing division before multiplication if division comes first). For example, in 10 / 5 x 2, some might do 5 x 2 = 10, then 10 / 10 = 1. | CORRECTION: Multiplication and Division have equal priority. Solve them from left to right as they appear. In 10 / 5 x 2, first do 10 / 5 = 2, then 2 x 2 = 4.

MISTAKE: Forgetting to solve operations inside parentheses first. For example, in 3 x (4 + 1), students might do 3 x 4 = 12, then 12 + 1 = 13. | CORRECTION: Always complete all calculations inside parentheses (or brackets) before doing any operations outside them. In 3 x (4 + 1), first do 4 + 1 = 5, then 3 x 5 = 15.

Practice Questions

Try It Yourself

QUESTION: Solve: 7 + 3 x 4 | ANSWER: 19

QUESTION: Solve: 20 - 10 / 2 + 5 | ANSWER: 20

QUESTION: Solve: 6 x (8 - 3) + 12 / 4 | ANSWER: 33

MCQ

Quick Quiz

Which operation should be performed first in the expression: 15 - 3 x (2 + 4) / 2?

Subtraction

Multiplication

Parentheses (Addition)

Division

The Correct Answer Is:

According to the order of operations (BODMAS/PEMDAS), operations inside parentheses must always be performed first. So, (2 + 4) should be solved first.

Real World Connection

In the Real World

When you use a calculator app on your phone or computer, it uses the order of operations to give you the correct answer. Even financial apps like Google Pay or banking apps use these rules for calculating interests or transaction totals, ensuring everything adds up correctly.

Key Vocabulary

Key Terms

OPERATION: A mathematical action like addition, subtraction, multiplication, or division. | PARENTHESES: Brackets like ( ) used to group parts of an expression. | HIERARCHY: The order of importance or priority for operations. | EXPRESSION: A mathematical phrase that contains numbers, variables, and operations. | EQUATION: A statement that two mathematical expressions are equal.

What's Next

What to Learn Next

Great job understanding the order of operations! Next, you can explore working with exponents (powers) and square roots, which also have their place in the order of operations. This will help you solve even more complex math problems with confidence!