12 TM.75.G.2346: Conclusion
If you completed Activity 13 then you learned that 24 níg-sagšu of spelt can be purchased with 1 gú-bar of barley. Friberg suggests that TM.75.G.2346 is more than just a list of prices of spelt, but rather shows the Ancient Mesopotamian division process.[1] This is because the tablet could potentially be solution to the following question.
Question: if the price of spelt is 1 gú-bar of barley per 24 níg-sagšu, then how much barley is needed to purchase 10,000 níg-sagšu?
In modern terms, the solution is simply to divide 10,000 by 24. The tablet gives the answer incorrectly as 418 with a remainder of 4; the correct answer found in Activity 13 is 416½ with a remainder of 4.
While we can feasibly interpret TM.75.G.2346 as the answer to a division question, how can we understand the content of TM.75.G.2346 as a division algorithm? Take as an example 2600 divided by 9.
| Row | Dividend | Quotient | Remainder |
| 1 | 10 | 1 | 1 |
| 2 | 50 | 5 | 5 |
| 3 | 100 | 11 | 1 |
| 4 | 500 | 55 | 5 |
| 5 | 1000 | 111 | 1 |
| 6 | 2000 | 222 | 2 |
| 7 | 600 | 66 | 6 |
| 8 | 2600 | 288 | 8 |
The process starts by finding a small round number that we know how many times 9 goes into. In this case we start in Row 1 with 10. In Row 1, we list the dividend as 10, quotient as 1, and remainder as 1 because 10=9×1+1.
We then can increase the size of the dividend by multiplying by 5 or 2 working towards our goal dividend of 2600. We also multiply quotient and remainder by the same factor. For example, from Row 1 to Row 2 we multiply dividend, quotient, and remainder by 5. This reflects the fact that 50=9×5+5.
We continue the process with the one rule that we never list a remainder larger than 8. Because if a remainder is 9 or greater, we could have increased are quotient by 1. For example, from Row 2 to Row 3 we multiply dividend, quotient, and remainder by 2. Because multiplying the remainder 5 in Row 2 by 2 would give a remainder of 10, we take 9 from 10 and increase the quotient by 1. This reflects the fact that 100=9×11+1.
When we reach Row 5, we no longer need to follow the pattern and multiply by 5 since we only need to get to 2600. We instead multiply by 2 to get 2000. To get 600 in Row 6 we add Rows 3 and 4. And finally we get 2600 in Row 8 by adding together Rows 6 and 7.
Activity 14. The following is based on the tablet TM.75.G.1392[2] which is another Eblaite tablet that serves a similar purpose to TM.75.G.2346.
Divide 260,000 by 33 using the Eblaite method by filling in the table below.
| Dividend | Quotient | Remainder |
| 100 | ||
| 1000 | ||
| 10,000 | ||
| 100,000 | ||
| 200,000 | ||
| 60,000 | ||
| 260,000 |