In Nyeong Chang sent us the solution to the
two divisions set in the problem, set out using Galley Division,
and explained a little about how it works:
Not only are the answers same as when the long division method was
applied, but the same numbers are appearing. This works because the
basic mechanism of division is the same. What is done in both long
division and Galley division is seeing how many of the divisor can
fit into the dividend one digit at a time, and then calculating the
remaining number, and repeating until a remainder smaller than the
divisor is left.
Mao Yamamoto worked out $76254 \div 35$
rather than $235$ but showed very nicely how the standard long
division method relates to the Galley Division method by setting
out the Galley Division in the same way:
The method works in the same way as our modern methods of division.
The only difference is that when the denominator is more than one
digit and subtraction is needed, denominators are separated as one
digit and calculated. For example, in the calculation $76254 \div
35$ below, in the modern method we need to multiply $35$ by $2$ and
subtract from $76$. In Galley division, we multiply $3$ by $2$ and
subtract from $7$. Then we multiply $5$ by $2$ and subtract from
Compared with the modern methods of division, this Galley Division
may be easier for some students as it allows them to subtract
numbers with fewer digits.