!!! This appendix is not nearly done yet and we’re just moving pieces here as they seem appropriate. !!!
Multiplication notation
Infrequently in Middle Egyptian a number symbol would be written above a number of ones marks (or occasionally other symbols) and produce a more multiplication-based notation. This could produce numbers over one million:
𓆐 𓂭
𓐀𓏼
7×100,000 + 3×10,000 = 730,000
𓆐
𓍢𓏺
101×100,000 = 10,100,000
Fractions
In general, Egyptian fractions could be written by putting 𓂋 r above a number: 𓂋𓍤 ¹⁄₃₀₀. A few basic fractions had special symbols: 𓐞 ½ (transl. gs), 𓏴 ¼ (also written 𓂋𓏽) , 𓂌 ⅔ (rwj), 𓂍 ¾ (ḫmt-rw).
The Egyptians could only write unit fractions, that is fractions with 1 for a numerator (except for ⅔ and ¾). For any other fraction with a higher numerator, it had to be split into multiple fractions: to write ²³⁄₅₀, one must expand it into unit fractions:
²³⁄₅₀ is more than ⅓ but less than ½, so we take ⅓ from it;
²³⁄₅₀ – ⅓ = ⁶⁹⁄₁₅₀ – ⁵⁰⁄₁₅₀ = ¹⁹⁄₁₅₀, which is a bit more than ⅛, which we take from it;
¹⁹⁄₁₅₀ – ⅛ = ⁷⁶⁄₆₀₀ – ⁷⁵⁄₆₀₀ = ¹⁄₆₀₀.
So our total is ⅓ + ⅛ + ¹⁄₆₀₀ and would be written 𓂋𓏼𓂋𓐁𓂋𓍧. A lot of the Rhind Mathematical Papyrus is dedicated to expanding fractions.
Table of cardinal and ordinal number words
| Number | Cardinal (masc.) | Cardinal (fem.) | Ordinal (masc.) | Ordinal (fem.) |
|---|---|---|---|---|
| 1 | 𓌡𓂝𓏤 wꜥ | 𓌡𓂝𓏏𓏤 wꜥ | 𓁶𓊪𓏭 tpj | 𓁶𓊪𓏏 tpt |
| 2 | sn.wwj1 | sn.t | 𓌢𓈖𓏌𓅱𓏻 sn.nw | 𓌢𓈖𓏌𓅱𓏏𓏻 sn.nwt |
| 3 | ḫmt.w | ḫmt.t | ḫmt.nw | ḫmt.nwt |
| 4 | jfd.w | jfd.t | jfd.nw | jfd.nwt |
| 5 | dj.w | dj.t | dj.nw | dj.nwt |
| 6 | sjs.w | sjs.t | sjs.nw | sjs.nwt |
| 7 | sfḫ.w | sfḫ.t | sfḫ.nw | sfḫ.nwt |
| 8 | ḫmn.w | ḫmn.t | ḫmn.nw | ḫmn.nwt |
| 9 | psḏ.w | psḏ.t | psḏ.nw | psḏ.nwt |
| 10 | mḏw | mḏt | mḥ-10 | mḥt-10 |
| 11 | mḏw-wꜥ | mḏw-wꜥt | (etc.)2 | (etc.) |
| 12, … 19 | mḏw-sn.wwj, etc. | mḏw-sn.t, etc. | ||
| 20 | mḏwtj | mḏwtt | ||
| 30 | mꜥbꜣ | mꜥbꜣt | ||
| 40 | ḥmw | —3 | ||
| 50 | djjw | — | ||
| 60 | sjsjw | — | ||
| 70 | sfḫjw | — | ||
| 80 | ḫmnjw | — | ||
| 90 | psḏjw | — | ||
| 100 | — | št | ||
| 200 | — | štj | ||
| 1000 | ḫꜣ | — | ||
| 10,000 | ḏbꜥ | — | ||
| 100,000 | ḫfn | — | ||
| 1,000,000 | ḥḥ | — |
2. For all numbers above 9, the ordinal is mḥ or mḥt followed by the cardinal.
3. Cardinal tens from 40-90, and higher numbers except 100 and 200, have masculine only. 100 and 200 have feminine only.
Sidebar: The names of the numbers
As noted, the Egyptians rarely wrote the names of their numbers out, although they’ve been reconstructed as somewhat similar to English: ḫꜣ sfḫw-št ḫmnjw-psḏw “one thousand, seven-hundred, eighty-nine”. Note that all the components with two forms used the masculine (sfḫw-št, not *sfḫt-št) except the very last one, which could take the feminine form if it had one, if describing a feminine noun: ḫꜣ sfḫw-št ḫmnjw-psḏt.
The cardinals from 11 to 19 are compounds: mḏw-wꜥ … mḏw-psḏw “ten-one … ten-nine”. “200” had its own word štj listed above, but 2000 and 20,000 are compounds in reverse order: ẖꜣ snwwj, ḏbꜥ snwwj, probably because snwwj started out as a dual. The fact that 10,000 has its own word separate from 1000 means that large numbers get compounded differently: 120,000 is not “one hundred twenty thousand”, but “twelve ten-thousand”: mḏw-snwwj ḏbꜥ.
The glyph for “million” is the god ḥḥ Heh, god of infinity, but the number “one million” was possibly pronounced št ḏbꜥ “a hundred ten-thousands”, and so on: ḫmtw-št ḏbꜥ “three million”, literally “three hundred ten-thousands”.