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What is the Order of Operations with Numbers?
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 in a mathematical expression. It ensures everyone gets the same correct answer when solving problems with multiple operations.
Simple Example
Quick Example
Imagine you buy 2 packets of biscuits at Rs. 10 each and then a cold drink for Rs. 20. If you calculate 2 + 10 x 20, you might get 220. But if you follow the order of operations, you first multiply 10 x 2 (cost of biscuits) to get 20, and then add 20 (cost of cold drink) to get Rs. 40. The correct way gives the right bill!
Worked Example
Step-by-Step
Let's solve: 12 + 8 ÷ 2 - 3 x 4
Step 1: First, we look for division or multiplication from left to right. We see 8 ÷ 2.
8 ÷ 2 = 4
Our expression becomes: 12 + 4 - 3 x 4
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Step 2: Next, we see 3 x 4.
3 x 4 = 12
Our expression becomes: 12 + 4 - 12
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Step 3: Now we only have addition and subtraction left. We do them from left to right. First, 12 + 4.
12 + 4 = 16
Our expression becomes: 16 - 12
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Step 4: Finally, we do 16 - 12.
16 - 12 = 4
Answer: 4
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 rely on it for financial calculations. It's a foundational skill for many exciting careers!
Common Mistakes
MISTAKE: Doing addition/subtraction before multiplication/division. For example, in 5 + 3 x 2, calculating 5 + 3 = 8, then 8 x 2 = 16. | CORRECTION: Always perform multiplication and division before addition and subtraction. So, 3 x 2 = 6, then 5 + 6 = 11.
MISTAKE: Working from right to left for operations of the same priority. For example, in 10 - 4 + 2, calculating 4 + 2 = 6, then 10 - 6 = 4. | CORRECTION: For operations of the same priority (like addition/subtraction or multiplication/division), always work from left to right. So, 10 - 4 = 6, then 6 + 2 = 8.
MISTAKE: Ignoring parentheses or brackets. For example, in 2 x (3 + 4), calculating 2 x 3 = 6, then 6 + 4 = 10. | CORRECTION: Always solve operations inside parentheses or brackets first. So, 3 + 4 = 7, then 2 x 7 = 14.
Practice Questions
Try It Yourself
QUESTION: Solve 7 + 3 x 5 | ANSWER: 22
QUESTION: Solve 25 - 10 ÷ 5 + 2 | ANSWER: 25
QUESTION: Solve (15 + 5) ÷ 4 - 2 x 2 | ANSWER: 1
MCQ
Quick Quiz
Which operation should be performed first in the expression 18 ÷ 3 + 2 x 5?
Addition
Subtraction
Division
Multiplication
The Correct Answer Is:
C
According to the order of operations, division and multiplication have higher priority than addition and subtraction. When both are present, we work from left to right. So, division (18 ÷ 3) comes before multiplication (2 x 5) because it appears first from the left.
Real World Connection
In the Real World
When a railway engineer calculates the load a bridge can carry, they use complex formulas involving multiple operations. Incorrectly applying the order of operations could lead to wrong calculations and potentially unsafe designs. Even a simple app like a calculator or spreadsheet uses these rules to give you the correct totals for your monthly budget or grocery list.
Key Vocabulary
Key Terms
OPERATION: A mathematical action like addition, subtraction, multiplication, or division. | EXPRESSION: A mathematical phrase that contains numbers, operations, and sometimes variables. | PARENTHESES: Curved brackets ( ) used to group parts of an expression. | PRIORITY: The importance or order in which an operation should be performed.
What's Next
What to Learn Next
Great job understanding the order of operations! Next, you can explore how to use exponents and square roots within these rules. This will help you solve even more complex problems and prepare you for algebra!
