3096 1800 100 times 18. ---- 1296 900 50 times 18. ---- 396 360 20 times 18. ---- 36 36 2 times 18. ---- 0 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 than 26 times; therefore, Twice 135 ” 3 ” 52 or twice 26 times. 10 times 135 ” 3 ” 260 or 10 times 26 50 times 135 ” 3 ” 1300 or 50 times 26 472 contains 18 more than 21 times; therefore, 4720 contains 18 more than 210 times, 47200 contains 18 more than 2100 times, 472000 contains 18 more than 21000 times, 32 contains 12 more than 2 times, and less than 3 times. 320 ” 12 ” 20 30 3200 ” 12 ” 200 300 32000 ” 12 ” 2000 3000 &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. [10] If you have any doubt as to this expression, recollect that it means “contains more than two eighteens, but not so much as three.”