122. Copy, as follows, examples with one figure in the divisor from the above Table, and perform the work in each case by Short Division. Three Figures in the Dividend. 1. Commence opposite 2, and take the numbers for the dividends from the columns in the same manner and order as was done in multiplication. 2. Take as divisor the figure immediately above the righthand figure of the dividend. The first six examples from columns A, B, C, are: Five Figures in the Dividend. 1. Commencing opposite 2, take the dividends from columns A, B, C, D, E; B, C, D, E, F; C, D, E, F, G; D, E, F, G, H; E, F, G, H, I; and F, G, H, I, J. 2. Take as divisor the figure immediately above the righthand figure of the dividend. 123. 1. A party of eight boys went fishing; they had a boat for every two boys; how many boats had they? SOLUTION. They had as many boats as 2 boys are contained times in 8 boys, which is 4. Hence they had 4 boats. 2. Justus earns 6 cents a day; how many days must he work to earn 24 cents? 3. A man buys 54 pounds of sugar; how many weeks will it last, if his family use 9 pounds a week? 4. There are 36 windows on one side of a building, arranged in 6 rows; how many windows in each row? 5. How many ranks of 6 soldiers each will 24 soldiers make ? 42 soldiers? 54 soldiers? 72 soldiers? 6. At 8 dollars apiece, how many trunks can be bought for 32 dollars? For 56 dollars? For 88 dollars? 7. When 5 plows cost $40, what is the cost of 3 plows? SOLUTION.-If 5 plows cost $40, one plow will cost as many dollars as 5 is contained times in 40, which is 8. Hence, one plow costs $8. Three plows will cost 3 times $8, which is $24. Hence, etc. 8. Daniel paid 28 cents for 4 oranges, and Luke bought 7. at the same price; how much did Luke pay for his? 9. If you can earn 56 dollars in 8 weeks, how much can you earn in 6 weeks? 10. When 5 yards of cloth can be bought for 20 dollars, how many yards of the same cloth can be bought for 32 dollars? 11. When 88 dollars will pay for 11 barrels of flour, how many barrels can be bought for 64 dollars? 124. 1. A father left $4925, which he wished to be divided equally among his two sons and three daughters; how much did each one receive? Ans. $985. 2. At $3 a cord, how many cords of wood could be bought for $693? For $906? Answers. 231; 302. 3. If a man walk at the rate of 4 miles an hour, in how many hours can he walk 840 miles? Ans. 210 hours. 4. How many barrels of flour can be made of 588 bushels of wheat, if it takes 4 bushels to make a barrel? Ans. 147. 5. A certain laborer saves $6 a month; how many months will it take him to save $726? Ans. 121 months. 6. How long will a man be employed in cutting 175 cords of wood, if he cut 7 cords each week? Ans. 25 weeks. 7. How many baskets, each of which holds 6 pecks, would be needed to hold 804 pecks of apples? Ans. 134. 8. There are 604800 seconds in a week; how many seconds in one day? Ans. 86400 seconds. 9. How many revolutions will be made by a wheel 11 feet in circumference, in running one mile, which is equal to 5280 feet? Ans. 480. 10. A man distributed $423 among poor persons, giving each $9; how many persons received the money? Ans. 47. 11. A furniture dealer expended $413 in purchasing chairs at $7 a dozen; how many dozen did he buy? 12. A farmer sold 184 bushels of wheat at $1.50 per bushel, and expended the amount received in buying sheep at $4 a head; how many sheep did he buy? 13. A merchant expended $534 in purchasing boots at $6 a pair, which he sold at $8 a pair; how much did he gain on the transaction? 14. A grain dealer sold 912 bushels of corn at $.75 a bushel, and expended the amount received in buying flour at $9 a barrel; how many barrels of flour did he purchase? 125. STEP I.-Examples with one order of units in the quotient, where the quotient figure can be found at once by dividing by the left-hand figure of the divisor; thus, Divide 13600 by 34. 34) 13 600 (400 13600 Here observe that 3, the left-hand figure of the divisor, is contained 4 times in 13, the two left-hand figures of the dividend, and that 34 multiplied by 4 equals 136. Hence 34 is contained 4 times in 136, and, according to (115), 400 times in 13600. 126. Divide and explain each of the following examples: 127. STEP II.-Examples with one order in the quotient, where the quotient figure must be found by trial. In examples of this kind, we proceed thus: Divide 1769 by 287. FIRST TRIAL. 287) 1769 (8 2296 SECOND TRIAL. 287) 1769 (7 2009 1. We divide as before by 2, the left-hand figure of the divisor, and find the quotient 8. This course will always give the largest possible quotient figure. Multiplying the divisor 287 by 8, we observe at once that the product 2296 is greater than the dividend 1769. Hence 287 is not contained 8 times in 1769. 2. We erase the 8 and 2296 and try 7 as the quotient figure. Multiplying 287 by 7, we observe again that the product 2009 is greater than the dividend 1769. Hence 287 is not contained 7 times in 1769. THIRD TRIAL. 287) 1769 (6 1722 47 than the divisor 287. remains. 3. We erase the 7 and 2009, and try 6 as the quotient figure. Multiplying 287 by 6, we observe that the product 1722 is less than the dividend 1769. Subtracting 1722 from 1769, we have 47 remaining, a number less Hence 287 is contained 6 times in 1769 and 47 EXAMPLES FOR PRACTICE. 128. Find the quotients and remainders in each of the following: 129. PROB. II.-To divide any number by any given divisor. divide the number thus found by the divisor. 2 tens annexed to 380 tens make 382 tens. 59 is contained 6 times in 382, with a remainder 28, hence, according to (115—1), it is contained 60 times in 3820, with a remainder 280. 3. We annex the next lower figure and proceed as before. |