Elementary arithmetic, with brief notices of its history... by Robert Potts.

34
III.
1. 18. 2. 19,001. 3. 445,545. 4. 907583. 5. 1,549830. 6. 76,543211.
7. 254,241,976. 8. 104,734222. 9. 2,922,930923.
IV.
1. The number is 85,018982. 2. 495799. 3. 846,055. 4. 4,876491,781190.
5. 944813. 6. 30576. 7. 229,495,326. 9. 49,999940,000050,060000.
V.
1. See Art. 5. 2. See Art 5. 4. 666269. 5. The numbers are 348 and 173.
6. 54365,636568.
VI.
1. Exlcess is 1131138. 2. 313618. 3. 32063. 4. 6693,878.
MULTIPLICATION AND DIVISION.
I.
1. Art. 1. 2. Art. 4. 3. Art. 4. 4. Art. 4. 5. Art. 2. 6. Art. 5: Art. 4,
note.
II.
1. 657152: 7139954304: 1261948567.
2. 12851451688656: 987632423577.
3. 67500: 3106800: 3145200000.
4. 70997476000000: 54839483410.
5. 659271431415. 6. 3427042396305224424960.
III.
1. The multiplier 729819 is obviously composed of 729, 81 and 9, or 9, 9 X9 and
9X81. If these three products of the multiplicand be found, and added together
according to their local values, the amount will be the product obtained by 3 lines of
multiplication instead of 6. A similar remark applies to the other 5 examples.
IV.
2. 87 times. 3. Multiply the given number by 20. 4. 648G640+8. 5.
492 = 500-8, multiply by 500 and by 8, and take the difference. 6. The quotients
of 500000 and 1000000 by 4389 will give the limits. 7. See pp. 5, 6, Section I.
8. 86.
V.
1. Art. 1. 2. Art. 1. 3. See Art. 13. 4. Art. 9. 5. Art. 10.
6. 8+7=5X3, 10-4=30-5, or A-.
VI.
l. Quot. 1872843, rem. I: quot. 1248562, ren. 1: quot. 936421, rem. 3: quot.
749137, rem. 2: quot. 621281, rem. 1: quot. 535098, rem. 1: quot. 468210, rem. 7:
quot. 416187, rem. 4.
2. Quot. 587668, rem. 46: quot. 449944, rem. 62: quot. 239970, rem. 78: quot.
218155, rem. 18.
3. Quot. 424, rem. 596: quot. 42, rem. 15956: quot. 4, rem. 92756.
4. Quot. 418, rem. 300000: quot. 168, rem. 8.
5. Quot. 999, rem. 1: quot. 139, remi. 119805.
6. Quot. 253, rem. 4807. 7. Quot. 777, rem. 2100.
8. Quot. 30939964, rem. 8: quot. 2812723, rem. 98: quot. 278738, rem. 413:
quot. 27848, rem. 7523: quot. 2784, rem. 62459.