Therefore 156 contains 13 10 + 2, or 12 times.

Again, to divide 3096 by 18.

Therefore 3096 contains 18 100 + 50 + 20 + 2, or 172 times.

77. You will now understand the following sentences, and be able to make similar assertions of other numbers.

450 is 75 × 6; it therefore contains any number, as 5, 6 times as often as 75 contains it.

135 contains 3 more than26times; therefore,
Twice 135”3”52or twice 26
10 times 135”3”260or 10 times 26
50 times 135”3”1300or 50 times 26
472contains 18 more than21times; therefore,
4720contains 18 more than210times,
47200contains 18 more than2100times,
472000contains 18 more than21000times,
32contains 12 more than2times, and less than 3 times.
320”12”20times, ”  ” 30 times.
3200”12 ”200times, ”  ” 300 times.
32000”12”2000times, ”  ” 3000 times.
&c. &c.&c. 

78. The foregoing articles contain the principles of division. The question now is, to apply them in the shortest and most convenient way. Suppose it required to divide 4068 by 18, or to find 4068/18 (23).

If we divide 4068 into any number of parts, we may, by the process followed in (74), find how many times 18 is contained in each of these parts, and from thence how many times it is contained in the whole. Now, what separation of 4068 into parts will be most convenient? Observe that 4, the first figure of 4068, does not contain 18; but that 40, the first and second figures together, does contain 18 more than twice, but less than three times.[10] But 4068 (20) is made up of 40 hundreds, and 68; of which, 40 hundreds (77) contains 18 more than 200 times, and less than 300 times. Therefore, 4068 also contains more than 200 times 18, since it must contain 18 more times than 4000 does. It also contains 18 less than 300 times, because 300 times 18 is 5400, a greater number than 4068. Subtract 18 200 times from 4068; that is, subtract 3600, and there remains 468. Therefore, 4068 contains 18 200 times, and as many more times as 468 contains 18.