The Operation Proved. § 36. Subtraction may be verified or proved, by adding the difference to the less number; the sum must be equal to the greater number. EXERCISES. 1. William had 325 chestnuts, but gave James 148 of them. How many chestnuts had William left? The number left is the difference between 325 and 148. Ans. 177 chestnuts. 2. A person who undertook a journey of 735 miles, has traveled 93 miles of the distance. What distance has he yet to travel? Ans. 642 miles. 3. From a farm which contained 2350 acres, 1234 acres were sold. How many acres remained of the original farm? 4. A young man received from his which he paid 2500 dollars for a house. the first sum had he remaining? 5. A merchant deposited 5800 dollars made a draft upon it for 3270 dollars. 6. Suppose a farmer who has 4000 granary, should take out 2100 bushels how many bushels would remain ? Ans. 1116 acres. father 5325 dollars, of How many dollars of Ans. 2825 dollars. in bank, but afterwards What sum remained? Ans. 2530 dollars. bushels of wheat in his to be sent to market; Ans. 1900 bushels. 7. A vintner bought 4036 gallons of wine, and afterwards sold at different times to the amount of 2373 gallons. How many gallons had he remaining? Ans. 1663 gallons. 8. Suppose I should borrow of my neighbor 1000 dollars, and three months afterwards should pay him 385 dollars of the debt; what balance would still be owing? Ans. 615 dollars. 9. A drover bought cattle for 1495 dollars, and sold the same at a loss of 270 dollars. For what sum did he sell them? 10. A gentleman sold a farm for 6700 530 dollars more than he gave for it. farm? Ans. 1225 dollars. dollars, which sum was What did he pay for the Ans. 6170 dollars. 11. A weaver made 30 pieces of cotton, containing 1200 yards; of which he has sold 17 pieces, containing 875 yards. How many pieces, and how many yards remain? Ans. 13 pieces; and 325 yards. 12. Bought of A 385 barrels of flour, and 2805 bushels of corn; of which I sold to B 109 barrels of flour, and 936 bushels of corn. What quantity of each remains unsold? Ans. 276 barrels of flour; 1869 bushels of corn. 13. A salter bought 35850 pounds of beef, and 150000 pounds of pork. Having exported 20500 pounds of the beef, and 75900 pounds of the pork, what quantity of each has he still on hand? Ans. 15350 pounds of beef; 74100 of pork. 14. A farmer raised 1200 bushels of wheat, and 213 bushels of oats. He sold to A 835 bushels of wheat, and 179 of oats, and the remainder of the crop to B. What amount of produce did the farmer sell to B? Ans. 365 bushels of wheat; and 34 of oats. 15. A merchant bought 375 yards of cloth, for 1645 dollars; of which he has sold 103 yards, for 685 dollars. How many yards of the cloth remain on hand, and for what sum must the remainder be sold, to lose nothing? Ans. 272 yards; and 960 dollars. 16. A grocer bought coffee for 420 dollars, and sugar for 545 dollars. He sold the coffee for 500 dollars, and the sugar for 603 dollars; what did he gain on each ? Ans. 80 dollars on the coffee; and 58 on the sugar. 17. Sold a lot of hams for 275 dollars-which made a profit of 43 dollars; and a lot of cheese for 305 dollars-which made a profit of 39 dollars. What did each kind cost me ? Ans. The hams, 232 dollars; the cheese, 266 dollars. 18. Four persons contribute towards the founding of a literary institution; A gave 2500 dollars, B 3300, C 375 less than A, and D 283 less than B. What were the sums contributed by C and D respectively? Ans. 2125 dollars by C; and 3017 by D. 19. Find the Difference 230469-85340. 20. Find the Difference 349130-94131. 21. Find the Difference 400500-80973. 22. Find the Difference 739745-76378. 23. Find the Difference 511839-84674. 24. Find the Difference 601813-13834. 25. Find the Difference 803460-45009. 26. Find the Difference 910311-87300. 27. Find the Difference 999830-99001. Ans. 145129. Ans. 254999. Ans. 319527. Ans. 900829. 28. A borrowed of B 8794 dollars; of which he paid to B at one time 2340 dollars, and at another time 1375 dollars. What balance remains to be paid? From the whole debt subtract the first payment, and from the remainder subtract the second payment. Ans. 5079 dollars. 29. A person who set out on a journey of 900 miles, traveled the first week 255 miles, and the second 233 miles. How many miles then remained to be traveled? Ans. 412 miles. 30. A testator provided in his will, that his estate, valued at 25479 dollars, should be divided as follows, viz: his only son to have 13500 dollars, his only daughter 5375 dollars, and his · widow the remainder. What sum did the widow receive? Ans. 6604 dollars. 31. A gentleman who owned a tract of land containing 15735 acres, sold from it, at different times, 3050 acres, 521 acres, 200 acres, and 2370 acres. How many acres of the tract had he then remaining? Ans. 9594 acres. 32. Borrowed of my neighbor at one time 175 dollars, at another 340 dollars, and at another 520 dollars. Having paid him 685 dollars, what balance have I yet to pay? From the sum 175+340+520, subtract 685. Ans. 350 dollars. 33. Put in store at one time 500 pounds of hemp; at another time 3800 pounds; and at another 2005 pounds. Having withdrawn 3473 pounds, what quantity remains in store? Ans. 2832 pounds 34. A merchant bought flour at one time for 325 dollars, and at another time for 460 dollars. Having become damaged, the whole was sold at a loss of 184 dollars; for what sum was it sold? Ans. 601 dollars. 35. A grocer purchased brandy for 195 dollars, and wine for 370 dollars. He sold the former at a loss of 35 dollars, and the latter at a loss of 80 dollars. What did he get for the whole ? Ans. 450 dollars. 36. A manufacturer sold two bales of cotton, which together contained 2000 yards. The first bale containing 985 yards, how many yards were in the second bale? Ans. 1015 yards. 37. A bought of B 875 acres of land, for 23400 dollars. For 500 acres of the tract, he paid 11379 dollars; how many acres were in the remainder of the tract, and for what sum was it purchased? Ans. 375 acres; and 12021 dollars. 38. One farmer had two fields of corn, each producing 230 barrels; and another had three fields, each producing 195 barrels. Which of the two raised the larger crop, and by how many barrels ? Ans. The second, by 125 barrels. 39. Three persons, A, B, and C, propose to purchase a manufactory, valued at 25850 dollars. A agrees to pay 5000 dollars, B twice as much as A, and C the remainder; what sum will C have to pay? Ans. 10850 dollars. 40. A merchant exchanges a stock of goods worth 6725 dollars, and a house worth 3120 dollars, with a farmer, for a tract of land valued at 5900 dollars,-the deficiency on the part of the land to be made up in money. What sum will the inerchant receive? Ans. 3945 dollars. 41. A has 2070 dollars more than B, and 375 dollars less than C, who has 4000 dollars; what sum then has B ? Ans. 1555 dollars. 42. Two travelers start together from the same place, and journey in the same direction, for three successive weeks,— the first at the rate of 240, the second 275 miles, per week; how far are the travelers apart at the end of the time named ? Ans. 105 miles. 43. Having 4800 dollars on hand, I wish to add to this a sum which will enable me to purchase a farm at 5390 dollars, and leave 300 dollars for other purposes. Required the sum to be added to the first one. Ans. 890 dollars. 44. A planter sold cotton amounting to 3460 dollars, and out of these proceeds purchased groceries for 150 dollars, and other provisions for 375 dollars. How much of the first sum had he remaining? Ans. 2935 dollars. 45. A cabinet maker sold furniture to the amount of 4000 dollars, and received, in part payment, at different times, 100 dollars, 200 dollars, 475 dollars and 904 dollars. How much of the debt remains to be paid? Ans. 2321 dollars. 46. A says to B, "in my fruitful pastures, I have 300 fat B replies, "then I have 120 more than you." Says C, "I lack but 35 of having as many as you both." many had C? oxen." How Ans. 685 oxen. 47. In 1820, the population of the United States was 9 millions, 638 thousand, one hundred and sixty-three; in 1830, it was 12 millions, 856 thousand, one hundred and sixty-five; and in 1840, 17 millions, 63 thousand, three hundred and fifty-three. What was the increase from 1820 to 1830, and what from 1830 to 1840 ? 3218002, from 1820 to 1830: 4207188, from 1830 to 1840. Ans. 48. The population of Europe being estimated at 238 miltions, 473 thousands, 957; of Asia at 390 millions; of Africa at 65 millions; of Oceanica at 20 millions; of N. America at 35 millions; and of S. America at 15 millions, 240 thousand;how much does the population of Asia exceed that of all the other grand divisions of the Earth? Ans. 16286043 inhabitants. MULTIPLICATION. § 37. MULTIPLICATION consists in finding the sum or product of a number taken any given number of times. The number multiplied is called the multiplicand; and the multiplying number, the multiplier; the two together are also called the factors of the product. Thus, 3 times 5 is 15; then 3 is the multiplier, 5 the multi plicand, and 15 the product. Also 3 and 5 are the factors of 15. How many is 3 times 2? Which is the multiplicand? The multiplier? The product? The factors? How many is 3 times 3 ? 4 times 3? 5 times 3? 6 times 3? Addition and Multiplication. § 38. The addition of the same number to itself, repeatedly, is a multiplication of that number. Thus 5+5+5 is 3 times 5; the sum or product being 15. How many is 6+6, or twice 6? 6+6+6, or 3 times 6? Recite the elementary products, once 1 is 1, once 2 is 2, &c., twice 1 is 2, twice 2 is 4, &c., 3 times 1 is 3, 3 times 2 is 6 &c., as given from left to right in the Multiplication Table. 5 6 7 8 Once 1 2 3 4 54 is 60 is 66 is 72 63 is 70 is 72|is| 80 is 88 is 96 99 is 108 6 times is Glis 12 is 18 is 24 is 30 is 36 is 42 is 48 is 10 times is 10 is 20 is 30|is 40|is 50|is 60 is 70 is 80 is 90 is 100 is 110 is 120|| 99 is 110 is 121 is 132 10-|is 120 is 132 is 144|| |