Contractions in Division. 110. ILLUSTRATIVE EXAMPLE IX. Divide 12367 by 10; by 100; by 1000. 12367÷10 1236.7 12367 ÷ 100 = 123.67 12367 ÷ 1000 = 12.367 = If the decimal point be moved one place to the left, each figure will express a number 1 tenth as great as before (Art. 30); therefore, 1 tenth of 12367 is 1236.7. For a similar reason, 1 hundredth of 12367 is 123.67, and 1 thousandth of 12367 is 12.367. Hence, when the divisor is 10, 100, 1000, etc., we may find the quotient by moving the decimal point of the dividend as many places to the left as there are zeros in the divisor. 46. There are 100 cents in a dollar; how many dollars are there in 2742 cents? in 12367 cents? 1st Ans. $27.42. 47. How many dollars are there in 14863 cents? 48. There are 1000 mills in a dollar; how many dollars are there in 56849 mills? 49. Divide 25000 by 10, by 100, by 1000, and add the quotients. 50. Divide 380768 by 100, by 1000, by 10, by 10000, and add the quotients. 111. ILLUSTRATIVE EXAMPLE X. Divide 20864 by 6300. WRITTEN WORK. 63) 208.64 (3.31... Explanation. Since 6300 = 63 × 100, we may first divide by 100, obtaining 208.64 (Art. 110), and then divide this quotient by 63, as shown in the margin (Art. 106). NOTE. In cases where the exact remainder is wanted, the common form of written work is better. 189 196 189 74 63 63/00) 208|64 (31351 It may be abbreviated, as in the written work of this note. Explanation.-Indicate first, by a vertical line, the division by 100; this gives 208 for a quotient, and 64 remain. Dividing now 208 by 63, we have for a quotient 3, and 19 hundreds remain. Uniting the first remainder 64 with the last remainder 19 hundreds, we have for the entire remainder 1964. For other contractions of division, see Appendix, page 302. 112. Examples in Division. a. Divide 58643 by 9. Ans. 65158. b. At $8 apiece, how many sheep can be bought for $2595? Ans. 324 sheep; $3 remain. c. If the dividend is 86445 and the divisor 51, what is the quotient? = Ans. 1695. Ans. 4088. d. What is the quotient of 40076 ÷ 98 ? e. 48 times a certain number equals 38256. that number? What is Ans. 797. f. What number multiplied by 87 gives a product of $22446 ? Ans. $258. g. Divide 759000 by 10, by 1000, by 100, and add the quotients. Ans. 84249. h. What is the sum of 93600 divided by 20, and 93600 divided by 7200? i. How many are 493689 ÷ 47000 ? Ans. 4693. Ans. 102888 3689 Ans. 902. Ans. 22537. 1. The product of two factors is 5063; one of them is 83. What is the other? Ans. 61. m. The product of three factors is 28350; two of them. are 42 and 75. What is the third? Ans. 9. Ans. 261554. n. 3130548 + one fourth of 2700 what number? 12 = Examples with Decimals. o. Divide 42.8116 by 13. p. What is 1 ninth of $76.842 ? Ans. 3.2932. Ans. $8.538. q. What is the cost of each chair if 25 chairs can be bought for $247? Ans. $9.88. NOTE. The examples on this page embrace the principal varieties in form of examples in division. Examples for additional practice will be found on pages 61 and 63. 113. Applications. 51. If I travel 42 miles a day, in how many days can I travel 273 miles? 52. How many barrels are required to hold 5488 pounds of flour, if one flour-barrel holds 196 pounds? 53. How many days are there in 9684 hours? 54. How many days will it take a ship to sail 13724 miles, at the rate of 133 miles a day? 55. There are 5280 feet in a mile. How many miles high is Mount Everest, which is 29002 feet high? 56. A. B. bought a farm for $18785 at $95 an acre. How many acres were there in the farm? 57. A produce dealer packed 19152 eggs in boxes containing 144 eggs each. How many boxes did he fill? 58. If the dealer would put 19152 eggs into 84 equal-sized boxes, how many eggs should he put in a box? 59. In one year, Missouri produced 4164 tons of lead, worth $353940. What was the value of a ton? 60. There was sent to the U. S. Mint in 13 years $ 4377984 worth of gold. What was the average value sent a year? If gold was worth 16 dollars an ounce, and 12 ounces make a pound, how many pounds were sent ? 114. Examples with Decimals. 61. A man divided among his three sons 887.625 acres of land. What was each son's share? 62. What is the price of 1 comb, when 48 combs can be bought for $53.76 ? 63. When 234 oranges are bought for $7.02, what is paid for 1 orange? In the following examples continue dividing to the third order of decimals: 64. Find 1 ninth of 1.28 acres. (67.) 8.1 21 = ? (68.) 0.5÷33 ? SECTION VI. MISCELLANEOUS EXERCISES. 115. General Review, No. 1. 1. 287 +5 million + 36 thousand + 59481 = ? 2. Add 567 to the sum of the following numbers: 121, 232, 343, 454, 565, 676, 787, and 898. 3. The difference between two numbers is 95478. The larger number is 148769; what is the smaller? 4. Which of the two numbers 15672 or 10560 is nearer to 13465, and how much? 5. Take 987 from each of the following numbers, and add the remainders: 3644; 7573; 2432; 4001. 6. What number must be added to the difference between 58 and 7003 to equal 938000? 7. What number taken from the quotient of 1833000 ÷ 24 leaves 25 ? 8. What number equals the product of the three factors 1785, 394, and 624-48? 9. If 5872 be the multiplicand, and half that number the multiplier, what is the product? 10. If 4832796 is the product, and 1208199 the multiplicand, what is the multiplier ? 11. If 894869 is the minuend, and the sum of the numbers in the fifth example is the subtrahend, what is the remainder? 12. If 700150 is a dividend, and 3685 the quotient, what is the divisor? 13. If 28936 is the divisor, and 86 is the quotient, what is the dividend? 14. Divide 87 million by 15 thousand. For other questions in review, see pages 59-63. 116. Oral Examples for Analysis. (See Appendix, page 302.) a. If a car runs 69 miles in 3 hours, how far can it run in 5 hours? b. If 18 rows of potatoes yield 36 bushels, how many bushels will 20 similar rows yield? c. If $5 pay for 35 quarts of berries, how many quarts will $12 buy? d. If, when flour is $8 a barrel, a ten-cent loaf weighs 25 ounces, what should it weigh when flour is $10 a barrel? e. If 5 oxen consume 185 pounds of hay in 2 days, how much will be required for 1 yoke of oxen for the same time? f. If 6 cows were bought for $224 and sold for $260, what was the gain on each cow? g. If 150 barrels of apples were bought for $200 and sold for $350, what would be gained by selling 45 barrels at the same rate? h. I bought a lot of paint for $3.90 and sold it for $5.10, gaining 12 cents on a pound. How many pounds did I buy? i. If a quantity of hay lasts 22 oxen 10 days, how many days will it last 5 yoke? j. A field of wheat was reaped by 10 men in 6 days; what length of time would be required for 15 men to reap the same amount? k. A cistern can be emptied in 15 minutes by 7 pipes; in what time can it be emptied, if only 5 of the pipes are open? 1. If 8 operatives can do a piece of work in 12 days, in what time will 24 operatives perform the same work? m. If a certain piece of work can be performed by 50 men in 4 weeks, how many more must be employed to perform it in a week? n. Ten hunters have provisions to last them 6 weeks; if 2 men be killed, how long will the provisions last the remainder? |