Miscellaneous Examples, Chapters I and II. 1. Express in words 3015602, and in figures eleven million five hundred thousand two hundred fourteen. 2. Find the sum of 30157, 12.468, 31947, and 3.6539. 5. How many times can 317 be subtracted from 1389, and what is the remainder? 6. Express MDCCCLXXIX in the Arabic notation, and 1449 by means of Roman numerals. 7. Find 1325 + 3016 +79 + 90167. 8. Find 316 — 179 +257 — 89 - 185 + 398 — 485. 9. Multiply 1234 by 4321 and 9009 by 31562. 10. How many nineteens are there in five thousand, and how many are over? 11. By how much does the sum of 3.72 and 10.015 fall short of the sum of 7.216 and 6.52? 12. Express in words 1632057 and 3004167201500. 13. Subtract the sum of 3158, 2016, and 5143 from 11111. 14. Multiply the difference between seventy-six million seventy-six and four hundred forty thousand four hundred forty, by eleven hundred fourteen. 15. A farmer has 197 sheep and three times as many lambs. How many sheep and lambs has he altogether? 16. Find by short divisions how many thirty-fives there are in 31578, and how many are over. 17. Add 31.057, 156.0083, 2.61759, and .008347. 18. Subtract the difference between 3.14 and 1.0625 from the sum of 1.00172 and 2.127. 19. By how many is one million eight thousand nine hundred seventy-four less than two million eleven hundred twelve? 20. Find 3142 - 1250 - 989 + 6217 — 3587 — 1924. 21. A farmer had 2000 bags of wheat. He sold 527 bags to one man and 255 bags to each of three others. How many bags were left unsold? 22. How many letters are there in a book of 375 pages, each page of which contains 32 lines, and each line 45 letters? 23. Multiply 31.025 by .032, and .0625 by .00125. 24. By what number must 59755 be divided in order that the quotient may be 19? 25. Divide 7.0175 by 17.5, and 7.5 by .00625. 26. In one school there are one hundred seventy-six boys and one hundred and twelve girls; and in another school there are half as many boys and twice as many girls. How many scholars altogether are there in the two schools? 27. The sum of two numbers is 317205 and one of them is 185964; what is the other? 28. A farmer sold 75 cattle at 24 dollars a head and bought with the money sheep at 2 dollars each. How many sheep did he buy? 29. Divide .04312 by .0044, and 9.0225 by .225. 30. Divide 358 by 15 by short divisions. 31. What is the least number which must be added to 57914 in order that the sum may be exactly divisible by 315? 32. Divide the product of 37.5 and .1248 by .005625. 33. Express MDCCCXCIV in the Arabic notation, and 2875 by means of Roman numerals. 34. In a school of four hundred and ninety children there are two hundred and seventy-six girls. How many more girls than boys are there? 35. In a train there are 37 cars each having seats for 36 people, and there are 375 passengers in the train; how many seats are empty? 36. Simplify 1.702 × 2.9015÷÷.0005803. 37. Divide the product of .0374 and .0075 by the difference between .675 and .6375. 38. Show that the sum of the squares of three thousand nine, and four thousand twelve, is equal to the square of five thousand fifteen. 39. What is the least number which must be subtracted from 2146537 in order that the remainder may be exactly divisible by 4275? 40. Subtract nine hundred five million eight thousand nine hundred sixty-five from eleven hundred million two thousand three hundred, and express the result in words. 41. At an election, the successful candidate, who obtained 12597 votes, had a majority of 1479 over the unsuccessful candidate. How many votes were given altogether? 42. Find 2197 – 1982 +374 +10085 – 8216 + 11597 - 7986. 43. Find the squares of 2.15 and .0324. 44. Multiply 16777216 by 131072, also divide 16777216 by 131072, and express the results in words. 45. Find the least number of repetitions of 3745 whose sum is greater than a million. 46. Divide .378 by 262.5, and 37.8 by .02625. 47. Express the numbers 29, 47, 158, 679, 1464, and 10385 by means of Roman numerals. 48. How many figures are there in all the numbers from 1 to 100? How many in the numbers from 1 to 1000? 49. A certain number when divided by 3008 gives a quotient 3875 and a remainder 2794. What is the number? 50. Divide 999999 by the continued product of 3, 7, 11, and 13. 51. The sum of two numbers is 315642, and one of the numbers is twice the other: find them. 52. Divide 2722.05 by .345, and .0272205 by 3.45. 53. Divide (144.4 +152 x 4.6) by 19; prove your answer by dividing after uniting the terms of the dividend. 54. Divide, by factors, (6.3 × 6+ 4.9 × 18) by 21. See Art. 44 for definition of factors. CHAPTER III. FACTORS AND MULTIPLES-SQUARE ROOT-HIGHEST COMMON FACTOR-LEAST COMMON MULTIPLE. FACTORS. 74. AN exact divisor of a number is called a Factor of that number; thus, 2, 3, 4, 6, and 12 are factors of 24. [Art. 44.] A factor is also called a Measure. A number that is exactly divisible by another number is called a Multiple of that number; thus, 12, 30, 54, 72, and 90 are multiples of 6. It will be seen at once that a number has a limited number of factors, but an unlimited number of multiples. 75. A number which is not divisible by any number except itself and 1 is called a Prime Number, or a Prime. Thus, 2, 3, 5, 7, etc., are primes. Every number which has other factors beside itself and unity is called a Composite number. Thus, 4, 6, 8, 9, etc., are composite numbers. Two numbers, both of which cannot be divided by the same number (except unity), are said to be prime to one another. Thus, 4 and 9 are prime to one another; both, however, are composite numbers. |