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What is an Order of Operations?
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 expressions with multiple operations like addition, subtraction, multiplication, and division. It ensures everyone gets the same answer for the same problem, just like following traffic rules keeps everyone safe on the road.
Simple Example
Quick Example
Imagine you are buying 3 samosas at Rs. 15 each and 2 chai at Rs. 10 each. To find the total cost, you first calculate the cost of samosas (3 x 15) and chai (2 x 10) separately, then add them. You wouldn't add 15 and 2 first, right? This is an everyday example of following an order.
Worked Example
Step-by-Step
Solve: 10 + 4 x 3 - 6 / 2
Step 1: Identify the operations. We have addition, multiplication, subtraction, and division.
---Step 2: According to the order of operations, we do multiplication and division first, from left to right. First, 4 x 3 = 12.
So, the expression becomes: 10 + 12 - 6 / 2
---Step 3: Next, perform the division: 6 / 2 = 3.
So, the expression becomes: 10 + 12 - 3
---Step 4: Now, perform addition and subtraction from left to right. First, 10 + 12 = 22.
So, the expression becomes: 22 - 3
---Step 5: Finally, perform the subtraction: 22 - 3 = 19.
Answer: 19
Why It Matters
Understanding the Order of Operations is crucial in fields like Computer Science and Engineering, where even small calculation errors can lead to big problems in software or structures. Data Scientists and Economists use it to correctly interpret complex formulas, ensuring their models and predictions are accurate. It's the foundation for all advanced mathematical calculations.
Common Mistakes
MISTAKE: Solving operations from left to right without considering their type (e.g., doing addition before multiplication). | CORRECTION: Always prioritize multiplication and division before addition and subtraction.
MISTAKE: Not performing multiplication and division (or addition and subtraction) from left to right when they appear together. | CORRECTION: When operations of the same priority (like multiplication and division) appear, always solve them from left to right.
MISTAKE: Ignoring parentheses or brackets and doing operations inside them last. | CORRECTION: Operations inside parentheses or brackets must always be solved first, before any other operations outside them.
Practice Questions
Try It Yourself
QUESTION: Solve 5 x 2 + 8 | ANSWER: 18
QUESTION: Solve 15 - 6 / 3 + 2 | ANSWER: 15
QUESTION: Solve (7 + 3) x 4 - 10 / 5 | ANSWER: 38
MCQ
Quick Quiz
Which operation should be performed first in the expression 12 + 6 / 3 - 2?
Addition
Subtraction
Division
It doesn't matter
The Correct Answer Is:
C
According to the Order of Operations, division and multiplication have higher priority than addition and subtraction. Therefore, 6 / 3 should be calculated first.
Real World Connection
In the Real World
When a financial analyst at a bank calculates interest on a loan or investment, they use complex formulas that strictly follow the Order of Operations to ensure the correct amount is calculated. Similarly, a software engineer coding a new feature for a mobile banking app like Google Pay or PhonePe relies on this order to make sure all transactions and calculations are processed accurately for millions of users.
Key Vocabulary
Key Terms
OPERATION: A mathematical action like addition, subtraction, multiplication, or division. | EXPRESSION: A mathematical phrase that contains numbers and operations. | PRIORITY: The importance or order in which an operation should be performed. | PARENTHESES: Brackets ( ) used to group parts of an expression, indicating they should be solved first.
What's Next
What to Learn Next
Great job understanding the basics! Next, you should explore working with expressions that include exponents and more complex brackets. This will help you tackle even bigger mathematical challenges with confidence.
