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.
Addition
Addition, called saṁkalita or saṁkalana in ancient India, is defined by Aryabhata II as 'the making into one of several numbers.' Various synonyms such as miśraṇa (mixing), sammelana (mingling), prakṣepaṇa (throwing together), saṁyojana (joining), ekikaraṇa (making into one), yoga (addition), and abhyāsa (practice) were used. In mathematical and astronomical works, addition was often taken for granted and briefly mentioned. Bhāskara II in Lilāvati instructs to add figures in the same places in direct or inverse order. The direct process involves writing numbers one below the other, adding digits starting from the units place, carrying over when sums exceed ten. The inverse process starts adding from the leftmost place, correcting partial sums as needed. For example, adding 26 and 57 by both methods yields 83. Exercises include performing addition of pairs like 37+49, 57+69, and 74+36 using these methods and verifying with modern addition.
📊 Diagram: Tables on page 5 illustrating direct and inverse addition processes with stepwise calculations.
🧪 Activity: Perform additions (i) 37+49, (ii) 57+69, (iii) 74+36 using direct and inverse methods and verify with modern addition.
🔗 Connection: Prepares for understanding subtraction, the complementary arithmetic operation.
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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