MISCELLANEOUS EXERCISES ON FRACTIONS.-ABBREVIATED MULTIPLICATION AND DIVISION. 1. Find the Sum, in units, of 13, 23, and 37. 2. Find the Sum, in units, of 17, 35, and 53. 3. Find the Sum, in units, of 3, 84, and 78. Ans. 181. Ans. 173. Ans. 18 4. Find the Difference, in fifths, between 75 and 313. Ans. 218. 5. Find the Difference, in sevenths, between 83 and 543. Ans. 200. 6. Find the Difference, in tenths, between 130 and 95,7. Ans. 343. 7. Reduce 52, 93, and 10 to improper fractions in their lowest terms. Ans. 11, 12, and 32. 8. Reduce 95, 10, and 13 to improper fractions in their lowest terms. Ans. 1, 2, and 53. 9. Reduce 72, 122, and 203 to improper fractions in their lowest terms. 10. Reduce 6, 102, and 123 to the least common denominator. Ans. 29, 6, and 101. improper fractions having Ans. 7, 122, and 152. 11. Reduce 83, 125, and 203 to improper fractions having the least common denominator. Ans. 140, 202, and 323. 12. Reduce 9, 10,7%, and 351 to improper fractions having the least common denominator. 13. One person expends 5 dollars for coal, at 7 dollars per ton; and another, 6 dollars, at 9 dollars per ton. them obtains the greater quantity of coal? Which of Ans. The first, by of a ton. 14. A paid 20 dollars for iron, at 37 dollars per ton; B 25 dollars, at 42 dollars per ton; and C 30 dollars, at 50 dollars per ton. Which of them bought the largest? and which the smallest quantity? Ans. C the largest, and A the smallest quantity. 15. Bought at one time 147 bushels of coal, and at another time 320 bushels. Having consumed 156 bushels, I desire to know what quantity of the coal purchased is still on hand. Ans. 31137 bushels. 16. From the sum of 1500 dollars which I deposited in bank, having drawn, at different times, 200 dollars, 1373 dollars, 313 dollars, and 793 dollars; what sum have I yet in bank? Ans. 7693 dollars. 17. Bought a quantity of iron for 95 dollars, and of coal for 81 dollars. The iron was sold for 1152 dollars, and the coal for 100 dollars; what profit was made on both commodities? Ans. 387 dollars.. 18. A merchant bought one piece of cloth containing 53 yards, another containing 393 yards, and another containing 40 yards. Having sold 13 yards, from the first piece, 242 from the second, and 19 from the third; he wishes to know the whole number of yards he has remaining. Ans. 76 yards. 19. A speculator bought 1000 acres of land for 1587 dollars, and 500 acres for 7377 dollars. Having sold 945 acres for 2000 dollars, he wishes to know how much land he has remaining, and for what sum he shall sell the remainder, so as to lose nothing on the whole. Ans. 554 acres; 32518 dollars. 20. Going out to collect money, I received from A 371⁄2 dollars, from B 20 dollars more than from A, from C 53 dollars more than from B, and from D as much as from the other three together. What was the whole sum collected? Ans. 316 dollars. 21. A contributed towards a charitable purpose 23 dollars, B contributed twice as much as A, C as much as B, D as much as A and B together, and E as much as all the rest. What was the whole contribution ? 22. Find the value of the expression (51 + 2 + 3 − 1 of 3) × 4. Ans. 376 dollars. 23. Find the value of the expression 24. Find the value of the expression 25. Find the value of the expression (254 + + − ‡ of 15) -: 26. Find the value of the expression (51 +4 of 3 of 3 of 20)÷ Ans. 25 Ans 532 3 Ans. 32 27. What will 163 acres of land amount to at 125 dollars per acre? 125 dollars × 163. third, When the Multiplier is one half, or one third, or one fourth, &c., of any number of tens, hundreds, or thousands, &c.; the operation may be abbreviated by taking those tens, hundreds, or thousands for the multiplier, and then taking the same part of the product thus obtained that the given multiplier is of the assumed one. Thus, in the present example, the multiplier 163 is of 100, since 6 times 16 is 100; the required product is therefore 125 × 100 125002083. Ans. 2083 dollars. 28. What should be paid for 2 tons of coal at 13 dollars a ton, 12 tons of hay at 27 dollars a wood at 7 dollars a cord? ton, and 33 cords of Ans. 6031 dollars. 29. What should be paid for 125 sheep at 3 dollars a head, 34 cows at 16 dollars a head, and 19 mules at 133 dollars a head? Ans. 35163 dollars. 30. Having on hand 193 tons of iron, if I sell 10 tons of it at 45 dollars a ton, and the remainder at 43 dollars a ton, what will the whole amount to? Ans. 871 dollars. 31. Paid 70 dollars for wood, at 2 dollars per cord; and afterwards sold of the quantity, at 31 dollars per cord. What did the wood sold amount to? Ans. 28 dollars. 32. If 3 masons can build a wall in 13 days, in what time ought one mason to build another wall of the same height and thickness, but 21 times as long? Ans. 914 days. 33. A speculator bought 189 acres of land at 10 dollars an acre, and 2501 acres at 13 dollars an acre. He sold of the first tract at 18 dollars an acre, and of the second at 19 dollars an acre; what would he gain on the whole by selling the remainder of both tracts at 20 dollars an acre? Ans. 335213 dollars. 34. How many tons of hay, at 16 dollars per ton, may be purchased for 246 dollars? 246 dollars 16 dollars. When the Divisor is one half, or one third, or one fourth, &c., of any number of tens, hundreds, or thousands, &c. ; the operation may be abbreviated by taking such equivalent improper fraction for the divisor. Thus, in the present example, the divisor 16 being equal to 100, we have 246100246 x 180=147 = Ans. 141 tons. 35. How many barrels of pork, at 12 dollars a barrel, may be purchased for 347 dollars? Ans. 27 barrels. 36. How many acres of ground, at 25 dollars an acre, may be bought for 1340 dollars? and how many at 75 dollars an acre may be bought for 3480 dollars? The divisors are equal to 100 and 300, respectively. 4 Ans. 53 acres; and 462 acres. 37. A sold to B 30 acres of land for 6221 dollars; and B sold to C 123 acres of the same land, at the same price per acre. What did C pay for the land he bought? 38. In how many days ought 14 men to accomplish a piece of work which 5 men could do in 33 days? Ans. 112 days. 39. Paid out 5915 dollars for silk at of a dollar per yard, and sold of the quantity purchased, at a profit of 3 of a dollar per yard. What did the part sold amount to? Ans. 421 dollars. 40. If 3 hundredweight of hemp sell for 161 dollars, what will 10 hundredweight bring at the same rate? 41. A bought of B 13 and of C 15 tons at 10 Ans. 53 dollars. tons of hay, at 9 dollars per ton, dollars per ton. He then sold to |