20. Divide 56 a x y z by 7 x y z. 21. Divide a by b. ANS. Here, the given quantities being dissimilar, the division cannot be performed, but only represented; we therefore write the divisor under the dividend, in the form of a fraction. 22. Divide x by y. 23. Divide a b by c x. 24. Divide 4 a b c by 5 x y. 25. Divide 17 a b x by 21 c d y. 26. Divide a b by a x. ab This may be written and then reduced, as in the answer, the two a's being cancelled. Let a = 4, b = 5, and x = 6; then a b = 4 × 5, and also reduce the result by dividing both terms by 7. 34. Divide 16 a b by 4 x. 35. Divide 20 a b by 4 a x. 36. Divide 15 x y by 5 a x y. 37. Divide 25 a b c m by 10 a b x. 38. Divide 18 a b fm by 6 a b ƒ m n x. 42. Divide a bf g h by a fh x. 43. Divide 49 a b c x y by 7 a b c d mx. - 45. Divide 12 (ab+9) by 8 (a − b + 9). 46. What is the quotient of a b (19 + x − y) divided by b (19 + x ·y)? 47. Divide 12 a b (x - y + z) by 3 a (x − y + z). 48. Divide 4 (a b— 10+x) by 7 (a b — 10 + x). 49. Divide 3 (a y 12 b) by a (a y — 12 b). SECTION II. Signs in Division. The process of dividing one algebraic quantity by another, consists of two parts: the first is, to ascertain the proper expression of the quotient, in letters and figures; the other is, to determine the character of that expression, either as positive or negative. In the last section, the mode of dividing one simple quantity by another, was considered alone, without any regard to the signs. The mode of determining these, will form the subject of the present section. ANS. a. 1. Divide a b by b. In this example, both of the given quantities are positive. And the divisor, b, being +, the quotient, a, must be also; for, multiplied together, they must give the product + a b, that is, the dividend.、 But if we suppose the quotient to be-a, we shall have ab, which will give a b. Hence, + divided by + gives + in the quotient. Here, the divisor, b, being, the quotient, a, must be also; for a x b will give a b, and not + a b, which is the dividend. Hence, + divided by -, gives in the quotient. 3. Divide 16 a b x by 8 a x. 4. Divide 36 a hmny by 5. Divide 72 a b x y by 6. Divide a b x by 7. Divide 12 am n by --- a b x. 12 am n. 9axy. 4 am n. 8. Divide 16 a brz by 8 a br. 9. Divide 28 a bm np by-7 amp. In this example, as the dividend, a b, is a-quantity, and the divisor, b, is +, the quotient must be — ; divided by +, gives — in the quotient. 12. Divide 13. Divide 14. Divide 15. Divide 16. Divide 17. Divide -- 16 a x by 4 a x. 21 a b m n by 7 am n. y. Here, as the divisor is, the quotient must be +; for their product must produce the dividend, namely, - a b, which is the product of a x-b. But if + we suppose the quotient to be, then we shall have —a x − b = + a b, which is evidently wrong. ах 24. Divide 32 a b c y by - 8 ac 25. Divide 45 h m r x by -9 m x. 3 c. bcx by bc. From the preceding examples and remarks, we derive the following general RULE for the signs in Division: When the signs of the divisor and dividend are alike, the sign of the quotient is +; when they are ant alike, it is 32. Divide 64 a m x by 8 a m. 33. Divide 81 a b c m n by 9 a b c. 24. Divide 63 h m n p by 7hm. 35 Divide 34 a y by 12 a y. 35 Divide-21e b x y z by -9 1 b x. a Druric 42 h m x by 7 x. 1. Divide a b + a c by a. ANS. bc. We have here a compound quantity, a b + a c, to be divided by a simple quantity, a. We first divide a b by a, and the quotient is b; we then divide a c by a, and the quotient is c: that is, we divide each term of the compound quantity separately. 2. Divide 12 a c + 9 b c by 3 c. ANS. 4 a +3 b. 3. Divide 18 a x + 15 21 a b by 3 a. 4. Divide 3 a b c + 12 a b x — 9 a b by 3 a b. 5. Divide 10 a x 15 x by 5 x. 6. Divide a r x + a h x a by a x. a y + az by a. 8. Divide 6 a b + 12 a c by 3 a. |