When the divisor hath cyphers in its lowest place, cut off the cyphers (with a dash of the pen) and as many of the lowest figures of the dividend, and then divide the other figures of the dividend by the significant figures of the divisor, as before taught; and the figures cut off from the dividend must be brought down to the remainder, if not cyphers. Application. 56100(75489132 (1347 194 168 268 224 446 392 5432 Examples. [46] 2400) 72579482 [47] 3600) 7529176586 [48] 3000) 427587761 [49] 9000) 6876752871 [50] 9000) 4786560000( [51] 4720) 6843248 ( [52] 20) 3724865( [53] 37482000) 478652725814( When Case IV. When the divisor is such a number, that any two figures, (in the multiplication table) being multiplied together, will produce the said divisor. Rule. Divide the given number by one of these figures, and that quotient again by the other, which will give the quatient required, Note, If there be a remainder in the last division, it will be so many times the first divisor, which added to the first remainder (if any) will give the true one. Examples. [54] Divide 1206817 by 16. [55] 42768 by 48. [56] 14652 by 64. [57]74682 by 72. [58] 417681 by 81 [59] 34672 by 108. [60] 217904 by 120. [61] 14276 by 144 Case V. Division may be performed with much ease and certainty by constructing a table of the products of the divisor multiplied by the single figures, in the same manner as the table of the multiplicand was constructed (Page 30.) 7792592592 6913580247 8791023456 7201234568 8888888889 8888888889 The Use. The use of this table is very easily apprehended: For we find the first member of the dividend as before, viz. the same number of figures as the divisor hath, if the highest figures of the dividend be greater than the highest of the divisor, or 1 more, if less. Then look in the table for that product which is immediately next less than the first member of the dividend, and place it under the said member; and the figure in the column to the left-hand is the quotient figure, which is thus known, without any doubtful trials, as before. The rest of the work is the same, as in the common method before taught. This method may be of good use to a learner, and likewise in making large divisions. PROBLEMS, Resulting from the Comparison of the preceding Rules. Problem I. Having the sum of two numbers and one of them given to find the other. Subtract the given number from the given sum, and the remainder will be the number required. Example. Let 144 be the sum of two numbers; one of which is 96, the other is required. From 144 the Sum Take 96 the given number Remains 48 the other. Proof 144 Problem Problem II. Having the greater of two numbers, and the difference between it and the lesser given, to find the lesser, Subtract the one from the other. Example. From 144 the greater Take 96 the difference Remains 48 the lesser. Problem III. Having the lesser of two numbers given, and the dif ference between it and a greater, to find the greater. Add them together. Given { 96 the lesser number 48 the difference Sum 144 the greater number required.. Problem IV. Having the product of two numbers, and one of them given to find the other. Divide the product by the given number, and the quotient will be the number required. Let the product of two numbers be 144, and one of them 3; I demand the other? Having the dividend and quotient to find the divisor, Divide the dividend by the quotient. Cor. Hence we get another way of proving Division. D2 Problem Problem VI. Having the divisor and quotient given, to find the dividend. Multiply them together. Now by a due consideration and application of these problems only, the following questions may be resolved in a short and elegant manner, altho' some of them are generally supposed to belong to higher rates. QUESTIONS. 1. What number is that, which being added to 9709 makes 109017 Answ. 1192. 2. The lesser of two numbers is 9709, the difference between them is 1192; what is the greater? Answ. 10001. 3. What number must I multiply by 7 that the product may be 623? Answ. 89. 4. The product of two numbers is 31383450, and one of them 4050: the other factor is required? Answ. 7749. 5. What is the difference, and what the sum of six dozen dozen, and half a dozen dozen? sum 936. 6. The sum of two numbers is 300; What is their difference and product? 29044. Answ. diff. 792, the less 114: Answ. 132 and 7. The remainder of a Division sum is 423; the quotient 423; the divisor is the sum of both and 19 more: What then was the number to be divided? Answ. 366318. 8. There is a certain number, which being divided by 7, the quotient resulting multiplied by 3, that product di vided by 5, from the quotient subtract 20, to the remainder add 30, and half the sun shall make 35? Answ. 700. 35×2-30+20 × 5 × 7 3 9. What |