respective numbers by substituting it in the foregoing expressions, thus: 7th 8th of 4088933=305153. of 4088933=382373. of 4088933=440288. of 4088933=485333. of 845693 of 4088933 521369. of 4088933=550853. 9th 13 of 845693-2 of 4088933=575423. 10th of 845693-7 of 4088933=596213. = 3 If, instead of the constant number 845693, it were required to have the respective numbers, when increased by the above fractional parts of the others, equal to any other constant number, we must multiply these answers by the ratio of this new number to 845693. [For a complete algebraic solution of this, and all other analogous questions, see my ALGEBRA.] CHAPTER XIII. MISCELLANEOUS QUESTIONS. 85. WHAT are the prime factors of 2006? Ans. 2006=2x17×59. 2. Wt are the prime factors of 3742? Ans. 3742=2× 1871. 3. What is the greatest common measure of 720, 360, and 180? Ans. 22 x 32 x 5=180. 4. What is the greatest common measure of 420, 147, and 210? Ans. 3x7=21. 5. What is the least common multiple of 4, 16, 24, and 40? Ans. 24x3x5=240. 6. What is the least common multiple of 8, 36, and 100? Ans. 23 x 32 x 52=1800. 7. What are all the divisors of 376 ? Ans. 1, 2, 4, 8, 47, 94, 188, 376. 8. What are all the divisors of 23456? Ans. {1, 2, 4, 8, 16, 32, 733, 1466, 2932, 5864, 11728, 23456. 9. What is the number of the divisors of 7866? Ans. 2×3×2×2=24. 10. What is the number of the divisors of 1000? 13. Reduce the improper fraction 123 to a mixed Ans. 19. fraction. 14. Reduce 48 to a mixed fraction. Ans. 6%. 15. Reduce 67 17. What is the product of 35 into 3? Ans. 742. Ans. 112. Ans. 35 18. What is the product of into 10? 19. Reduce the compound fraction of to a simple fraction. 20. Reduce, 3, and, to fractions having a com 26. How many places of decimals will be required to express ? Ans. 4 places. 27. Find the compound repetend equivalent to. Ans. 0.0384615 32. What must be the length of a thread which will wind spirally about a cylinder of 4 feet in circumference, and 60 feet in length, the distance between each turn of the thread being 1 foot? Ans. 247-38, &c. feet. 33. If A can perform a piece of work in 10 days, B in 12 days, C in 16 days, then how many days will be required for all together to perform the work? Ans. 45. 34. A shepherd, in the time of war, fell in with a party of soldiers, who plundered him of half his flock, and half a sheep over; afterwards a second party met him, who took off half of what he had left, and half a sheep over; and, soon after this, a third party met him, and used him in the same manner, and then he had only five sheep left. It is required to find what number of sheep he had at first. Ans. 47 sheep. 35. Four persons, A, B, C, and D, spent 20 shillings in company, when A proposed to pay, B, C }, and D part; but when the money came to be collected, they found it was not sufficient to answer the intended purpose. The question then is, to find how much each person must contribute to make up the whole reckoning, supposing their several shares to be to each other in the proportion above specified. 36. A stationer sold quills at 10 s. 6 d. a thousand, by which he cleared of this money; but, growing scarce, he raised them to 12 s. a thousand. What did he clear per cent. by the latter price? Ans. 71 per cent. 37. How much can a person give for an annuity of $400, which has to run 12 years, if the interest be reckoned at 3 per cent.? Ans. $3981 602. 38. A debt, due at this present time, amounting to $1200, is to be discharged in seven yearly and equal payments. What is the amount of one of these payments, if the interest be calculated at 4 per cent.? Ans. $199.931. 39. An usurer lent a person $600, and drew up for the amount a bond of $800, payable in 3 years, bearing no interest. What did he take per cent., if compound 'nterest be taken into consideration? Ans. 10.06424 per cent. 40. A debtor, being unable to pay his debts, amounting to $12950, at once, agrees with his creditors to discharge this sum by monthly instalments, viz.: $600 the 1st month, |