Rod Calculus - Division

Division

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The animation on the left shows the steps for calculating

1. Place the dividend, 309, in the middle row and the divisor, 7, in the bottom row. Leave space for the top row.
2. Move the divisor, 7, one place to the left, changing it to horizontal form.
3. Using the Chinese multiplication table and division, 30÷7 equals 4 remainder 2. Place the quotient, 4, in the top row and the remainder, 2, in the middle row.
4. Move the divisor one place to the right, changing it to vertical form. 29÷7 equals 4 remainder 1. Place the quotient, 4, on top, leaving the divisor in place. Place the remainder in the middle row in place of the dividend in this step. The result is the quotient is 44 with a remainder of 1

The Sunzi algorithm for division was transmitted in toto by al Khwarizmi to Islamic country from Indian sources in 825AD. Al Khwarizmi's book was translated into Latin in 13th century, The Sunzi division algorithm later evolved into Galley division in Europe. The division algorithm in Abu'l-Hasan al-Uqlidisi's 925AD book Kitab al-Fusul fi al-Hisab al-Hindi and in 11th century Kushyar ibn Labban's Principles of Hindu Reckoning were identical to Sunzu's division algorithm.