# Vedic Maths - Introduction

**Vedic Mathematics** is a system of mathematics consisting of a list of 16 basic *sutras*, or aphorisms. They were presented by a Hindu scholar and mathematician, Bharati Krishna Tirthaji Maharaja, during the early part of the 20^{th} century.

The calculation strategies provided by Vedic mathematics are said to be creative and useful, and can be applied in a number of ways to calculation methods in arithmetic and algebra.

16 Sutras translated in English (from Sanskrit) are:

- By one more than the one before
- All from 9 and the last from 10
- Vertically and Cross-wise
- Transpose and Apply
- If the Samuccaya is the Same it is Zero
- If One is in Ratio the Other is Zero
- By Addition and by Subtraction
- By the Completion or Non-Completion
- Differential Calculus
- By the Deficiency
- Specific and General
- The Remainders by the Last Digit
- The Ultimate and Twice the Penultimate
- By One Less than the One Before
- The Product of the Sums
- All the Multipliers

It is amazing that with the help of Vedic Mathematics, you will be able to solve or calculate complex mathematical problems mentally.

### 1. By one more than the previous one

**Square of numbers ending in 5**

65 × 65 = (6 × (6+1)) 25 = (6×7) 25 = 4225

45 × 45 = (4 × (4+1)) 25 = (4×5) 25 = 2025

105 × 105 = (10 × (10+1)) 25 = (10×11) 25 = 11025

**When sum of the last digits is 10 and previous parts are the same**

44 × 46 = (4 × (4+1)) (4 × 6) = (4 × 5) (4 × 6) = 2024

37 × 33 = (3 × (3+1)) (7 × 3) = (3 × 4) (7 × 3) = 1221

11 × 19 = (1 × (1+1)) (1 × 9) = (1 × 2) (1 × 9) = 209