What is the Order of Operations?

S3-SA1-0780

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 which operation (like addition, subtraction, multiplication, or division) to do first when we have many operations in one math problem. It helps everyone get the same correct answer every time, just like following traffic rules helps prevent accidents.

Simple Example

Quick Example

Imagine you went to a shop and bought 2 packets of biscuits for Rs 10 each, and then bought a juice for Rs 20. If you calculate 2 + 10 x 20, you might get a wrong answer. The Order of Operations tells you to multiply the biscuit cost first (2 x 10 = 20) and then add the juice cost (20 + 20 = 40).

Worked Example

Step-by-Step

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

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

Answer: 18

Why It Matters

Understanding the Order of Operations is super important for building computer programs, analysing data, and even in fields like physics and economics. Engineers use it to design bridges, and data scientists use it to make sense of huge datasets from apps like YouTube or Swiggy. It's a foundational skill for many exciting careers!

Common Mistakes

MISTAKE: Doing addition or subtraction before multiplication or division. For example, in 5 + 3 x 2, calculating 5 + 3 = 8 first. | CORRECTION: Always do multiplication and division before addition and subtraction. So, 3 x 2 = 6, then 5 + 6 = 11.

MISTAKE: Solving operations from left to right without considering the rules. For example, in 10 / 2 x 5, calculating 2 x 5 = 10 first. | CORRECTION: When you have only multiplication and division (or only addition and subtraction), always work from left to right. So, 10 / 2 = 5, then 5 x 5 = 25.

MISTAKE: Forgetting to solve operations inside parentheses (brackets) first. For example, in 2 x (3 + 4), doing 2 x 3 = 6 first. | CORRECTION: Always solve everything inside the parentheses (brackets) before doing any other operations outside them. So, 3 + 4 = 7, then 2 x 7 = 14.

Practice Questions

Try It Yourself

QUESTION: Solve: 7 + 3 x 5 | ANSWER: 22

QUESTION: Solve: 20 - 10 / 2 | ANSWER: 15

QUESTION: Solve: (15 - 5) x 2 + 8 / 4 | ANSWER: 22

MCQ

Quick Quiz

Which operation should be done first in the expression 12 + (5 - 2) x 3?

Addition (12 + 5)

Subtraction (5 - 2)

Multiplication (2 x 3)

Addition (12 + 3)

The Correct Answer Is:

According to the Order of Operations, operations inside parentheses (brackets) must be solved first. So, (5 - 2) is the first step.

Real World Connection

In the Real World

When a bank calculates your loan interest, or when a cricket analyst calculates a player's strike rate using a formula, they use the Order of Operations. Even the apps on your phone, like UPI or Google Maps, use these rules behind the scenes to process calculations correctly and quickly.

Key Vocabulary

Key Terms

OPERATION: A mathematical action like addition, subtraction, multiplication, or division. | PARENTHESES: Brackets like ( ) used to group parts of an expression. | EXPRESSION: A mathematical phrase that contains numbers, operations, and sometimes variables. | PEMDAS/BODMAS: Acronyms to remember the order of operations.

What's Next

What to Learn Next

Great job learning the Order of Operations! Next, you can explore how to work with exponents (powers), which also have a specific place in the order. This will help you solve even more complex problems and build a stronger foundation in math!