Mathematics in India | Class 11 Knowledge Traditions Practices of India Notes
By ConceptScroll Team · Published on 17 July 2026 · 4 min read
Mathematics in India – this guide gives you a concise, exam-ready overview of Mathematics in India from Class 11 Knowledge Traditions Practices of India, written by ConceptScroll editors and reviewed against the latest NCERT textbook.
Subtraction
Subtraction, defined by Aryabhata II as 'the taking out of some number from the total,' was known by terms such as vyutkalita (made apart), sodhana (clearing), patana (causing to fall), and viyoga (separation). The remainder was called śeṣa (residue) or antara (difference). The minuend was sarvadhana or viyojya, and the subtrahend viyojaka. Bhaskara II instructs to subtract numbers according to their places in direct or inverse order. In the direct process, subtraction starts from the units place; if the digit in the minuend is smaller than the subtrahend digit, ten is borrowed from the next higher place, and the remainder is adjusted accordingly. The inverse process begins from the leftmost digit, correcting partial differences as needed. For example, subtracting 360 from 1000 involves borrowing tens successively. Exercises include performing subtractions such as 4000 - 230, 4325 - 567, and 345 - 56.
📊 Diagram: Explanation of subtraction process with examples on page 5 and 6.
🧪 Activity: Perform subtractions: (i) 4000 - 230, (ii) 4325 - 567, (iii) 345 - 56 using direct and inverse methods.
🔗 Connection: Leads to the next fundamental arithmetic operation: multiplication.
Table on page 5 (4×4)
| Step 1: | Step 2: | Step 3: | Step 4: |
|---|---|---|---|
| 2 6 | 2 6 | 2 6 | 2 6 |
| + 5 7 | + 5 7 | + 5 7 | + 5 7 |
| 1 3 | 7 13 | (7+1) 3 | 8 3 |
Table on page 5 (4×4)
| Step 1: | Step 2: | Step 3: | Step 4: |
|---|---|---|---|
| 2 6 | 2 6 | 2 6 | 2 6 |
| + 5 7 | + 5 7 | + 5 7 | + 5 7 |
| 7 | 7 13 | (7+1) 3 | 8 3 |
Frequently asked questions
1. How many fundamental operations were known to the ancient mathematicians? What are they?
The ancient mathematicians knew four fundamental operations. These are addition, subtraction, multiplication, and division.
2. Name the Ancient Indian Mathematicians and their period, who worked in Geometry and Trigonometry. Do you find any similarity between the ancient mathematical concepts and the present day mathematical concepts of Algebra, Geometry, and Trigonometry that you study? (You may also refer the literature given in the references).
Some notable Ancient Indian mathematicians who worked in Geometry and Trigonometry include Baudhayana (circa 800 BCE), Apastamba, and Aryabhata (5th-6th century CE). They contributed to the Sulbasutras which contain geometric constructions and early trigonometric ideas. Similarities include the use of geometric principles for constructions and the early development of sine tables which relate to modern trigonometry. Algebraic concepts such as solving equations also appear in their works.
3. (a) Do you think there is any difference in the process of performing the basic operations on numbers in the earlier period and the present system which you studied? (b) Which process do you feel easier? Why? Discuss with your friends.
(a) Yes, there are differences. Earlier systems often used different numeral representations (like Brahmi numerals) and calculation methods (such as using counting rods or pebbles). The present system uses the Hindu-Arabic numeral system with place value and zero, which simplifies calculations. (b) The present system is easier because of the place value system and the use of zero, which makes arithmetic operations more straightforward and less time-consuming.
4. Write at least three terms used by ancient mathematicians and give their meanings: (a) addition (b) subtraction (c) multiplication (d) division
(a) Addition: The process of combining two or more numbers to get their total. (b) Subtraction: The process of finding the difference between two numbers by removing the value of one from another. (c) Multiplication: The process of repeated addition of a number a specified number of times. (d) Division: The process of distributing a number into equal parts or groups.
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