ARITHMETIC (PART 1) EXAMINATION QUESTIONS (1) Express in figures the following numbers: (a) ten million nineteen thousand forty-two; (b) seventy thousand six hundred five; (c) five hundred sixty-two hundredths. (2) Express the following numbers in Roman notation: (a) 4068; (b) 44; (c) 657,903; (d) 1920; (e) 1888. (3) What is the sum of $18.04, $1.57, $197.85, $36.43, and $360.52? Ans. $614.41. (4) Seven barrels, with their contents, weigh respectively 297 pounds, 417 pounds, 226 pounds, 388 pounds, 293 pounds, 185 pounds, and 313 pounds; if they are all hoisted in an elevator at one time, and the elevator weighs 2309 pounds, together with two men, one weighing 148 pounds and the other 187 pounds, what is the total weight lifted? Ans. 4763 pounds. (5) From a pile of pulp weighing 12,882 tons, 2057 tons were removed on a certain day and 3836 tons on another day; how many tons remained in the pile? Ans. 6989 tons. (6) If 256,405 be subtracted from a certain number and the remainder is 700,999; (a) what is the number? (b) What number must be subtracted from 1,001,010 to give a remainder of 660,019? Ans. {(a) 957,404. (b) 339,991. (7) What is the product of 461, 217 and 865. Check the result by casting out 9's. Ans. 86,532,005. (8) If the quotient is 5077, the divisor is 6345, and the remainder is 2609, what is the dividend? Check by casting out 9's. Ans. 31,908,174. (9) If the dividend is 4,511,856, the quotient is 2803, and the remainder is 1829, what is the divisor? Ans. 1609. (10) There are 5280 feet in a mile; (a) how many miles in 408,806 feet? How many feet in 1894 miles? 2 (a) 77 miles. 280 Ans. {(a) 773318 (b) 10,000,320 feet. (11) There are five numbers: (1) 840, (2) 231, (3) 1728, (4) 2618, and (5) 1215; (a) which of these numbers are odd? (b) which are even? (c) which are divisible by 3? (d) by 6; (e) by 9; (f) by 12? (12) Referring to the last question, which of the numbers are divisible (a) by 2? (b) by 4? (c) by 8? (d) by 5? 5236 X 9 X 45 X 26 (13) Find the value of 91 X 135 X 88 by cancelation. Ans. 21. (14) A hogshead contains 63 gallons; how many hogsheads are ARITHMETIC (PART 2) GREATEST COMMON DIVISOR AND LEAST COMMON MULTIPLE 75. Greatest Common Divisor. The greatest common divisor of two or more numbers is the largest number that will exactly divide all of them. Thus, the greatest common divisor (usually abbreviated G.C.D.) of 36 and 48 is 12, because 12 is the largest number that will divide 36 and 48-it is the largest common factor of 36 and 48; also, 36 is the G.C.D. of 72, 108, and 144, because it is the largest common factor of those numbers. To find the G.C.D. of two numbers, find the product of their common factors; the work is usually arranged as follows: Find the 9 54, 216 b, 4 G.C.D.6 X 9=54 Ans. G.C.D. of 54 and 216. Write the numbers as shown in the margin, separating them by a comma, and then proceed as in short division. By Art. 72, 54 and 216 are both divisible by 9; divide as shown, obtaining 6 and 24 for the quotients. Both 6 and 24 are divisible by 6, the quotients being 1 and 4. The only factor common to 1 and 4 is 1, which has no effect on the G.C.D. Since 54 and 216 have the common factors 9 and 6, they are divisible by the product of these common factors, and the G.C.D. of 54 and 216 is 9 X 6 54. To prove the work, 54 ÷ 54 = 1, and 216 54 = 4. = 76. To find the G.C.D. of more than two numbers, proceed in exactly the same way as in Art. 75, remembering that the divisors must divide all the numbers. Thus, find the G.C.D. of 270, |
