13. The salary of the President of the United States is $50000; what is it per day? Ans. $137. 14. There are 3150 gallons in 50 hogsheads; how many gallons are there in one hogshead ? 15. The dividend is 582, the divisor 15, and the remainder 12; what is the quotient ? Ans. 38. 16. The three factors of a certain number are 35, 43, and 57; what is the number? 17. What is the cost of 554 acres of land, at $65 an acre ? 18. The wine gallon contains 231 cubic inches; how many cubic inches are in a hogshead of 63 gallons ? . 19. A drover bought 53 horses at $75 each, 25 cows at $21 each, 3458 sheep at $6 each: be sold them for $251 less than he paid ; for how much did he sell them ? Ans. 24997. 20. What number multiplied by 11 gives 638 ? REDUCTION OF FRACTIONS. . 15 2 2 302 303 63 90 2 48 100 120, 120, 120 Reduce to the least common denominator, 1. 1, $,$. Ans. 46, 48, 4 2. 3, 4, 5 Ans. , 1, 11. 3. 1, 4, . Ans. 10, 4. f of, off, and of %. Ans. 44, 45, 46. 5. 1 of 21, of 3), and 3 of 53. Ans. 4, 16, 256. 6. 1, 4, and Ans. 4, 5, R. %. , , and be Ans. te, te 8. 4, 5, 6, and a Ans. , 13, 14, 20 9. 5, 6, 4, 5, , and % Ans. ** 8, 26, 30, 385, 344, 348. 10. 11, 31, 41. Ans. 16, 2009 60 60 202 80 90 7 60 60 1. What is į of f? off? 4 of 4 ? } of f? of #? off ? 2. One-third of 6 is 4 of what number? 1? ? ? ??? * ? ? ? ? 1? 1? 3. One-third of 9 is of what number? 1? ? 1 ? B. 4? 3? 3? t? ? 1? 4. Two-thirds of 9 is of what number? į ? ? ? ? 를 7? 3? 1? to? 11? 10 ? 5. One-third of 12 is of what number? 1 ? 3? ? +? ? ? ? ? 1? 6. Two-thirds of 12 is of what number? 1? ?? #? 7? } ? ? ? ? 13? 7. One-fourth of 12 is of what number? 3? 3? 3? ? ? ? 10 ? 11? 1. ? 8. One-half of 12 is of what number? 1? 1? 1? // 1 ? ? ? ? ? ? ? 9. Three-fourths of 12 is į of what number? } ? ? ? ? ? ? ? ? 17 ? 15? 10. One-fourth of 16 is of what number? 1?? 1? 4? 3? 3? Bo? j? 15? 11. One-half of 16 is of what number? 1? ? ? 7 ? ? ? to ? 1 ? 1? 12. Three-fourths of 16 is of what number? 1? ? ? ? ? ? ? ? 1? 1? 13. One-third of 18 is 1 of what number? 1 ? ? ? ? ? ? ? 1?1? 14. Two-thirds of 18 is of what number? 3? į? 1 ? 출 1 ? ? ? ? ? 10 ? 11? 1? 15. What part of 1 is ? ? ? ? } 16. What part of 2 is ? ? ? ? 1 Ans. }, }, , to 17. What part of 3 is 3 ? ? ? ? ? Ans. t, 1, $, e, to 18. What part of 4 is 1 ? ? ? ? Ans. $, 4, 4, 4. 19. What part of $ is 1 ? ? ? ? ? 圣?? Ans. $, , , , 20. What part of 4 is 1 ? ? ? ? ? 圣 ?? Ans. I, 1, }, 41, 14. 21. What part of 5 is 1 ? ? ? ? ? Ans. to, to, to, zo, 4. 22. What part of 20 is 4 ? 5? 68? 10? 15 ? Ans. 3, 4, 5, 1, 4. 23. What part of 25 is 4 ? 5? 61? 10? 121 ? Ans. , 1, 1, $, . 24. What part of 100 is 4? 5? 6? 10 ? 121 ? 6 Ans. zł, zbo, to, . 25. What part of 54 is ? 11? 21? 3} ? 41? 51 3 Ans. t, f, PT, 1, RT. 26. What part of 64 is 1 ? À ? 11 ? 11 ? 11? Ans. as, , , 2, . 27. 1 is 4 of what number ? ? ? ? ? Ans. 9, 31, 21, 11, 13. 28. 5 is 4 of what number ? ? ? ? ? Ans. 35, 171, 115, 81, %. 5 1IT 5 29. 6 is of what number ? ? ? ? ? Ans. 42, 21, 14, 104, 8%. 30. yy is of what number ? ? ? ? ? Ans. 49, 241, 163, 124, 94 31. of 14 is of what number ? ? ? ? ? 1 Ans. 4, 6, 8, 10, 12. 32. of 14 is of what number ? ? ? ? ? Ans. 8, 12, 16, 20, 24. 33. of 14 is 1 of what number? ? 1 ? ? ? 를 Ans. 12, 18, 24, 30, 36. 34. of 15 is 4 of what number? } ? ? ? 1? Ans. 18, 27, 36, 45, 54. 35. of 15 is of what number? ? ? ? ? Ans. 24, 36, 48, 60, 72. MULTIPLICATION OF FRACTIONS. PROBLEMS, = 1. Multiply 1 by 1. # x1 = $; and by alternating, 1 x }=. 2. Multiply } by 1. }x1= }; and by alternating, 1 x } $ 3. Multiply 1 by 1. 1 x1= t; and by alternating, 1 x = 1. 4. Multiply 1 by 2. * x2 = ; and by alternating, 2 x t = $. X 5. Multiply f by 2. * x2 = $; and by alternating, 2 x } = f. 6. Multiply by 2. of 2. x 2 = 4; and by alternating, 2 xf = 4. $ 4. Multiply by 2. * x 2 = 4; and by alternating, 2 xf = $. 6 12: 8. Multiply 1 by : 1x1 = 1 1 9. Multiply } by to }x=1 10. Multiply k by t. fx} = . 11. Multiply by . ** = REM.—Multiplying 1 by 1 is the same as dividing it by 2, and multiplying it by } is the same as dividing it by 3; hence, to multiply a unit by a fraction whose numerator is unity, the product will have unity for its numerator, and the denominator of the fraction for its denominator ; if both factors are fractional, the product of their denominators is the denominator of the product; if the numerator of either factor is increased, the product is similarly increased. Cor.— The product of two or more fractions will have for its numerator the product of all the numerators, and for its denominator the product of all the denominators. DIVISION OF FRACTIONS. PROBLEMS. 1. Divide 4 by f. 2. Divide f by to 3. Divide by . 4. Divide { by 1. 5. Divide by . 6. Divide 1 by . 7. Divide 1 by ; $; 4; 8. Divide 1 by j ; * ; . 9. Divide 2 by f; ; 1; 10. Divide 2 by $; $; $. 11. Divide by }; }; $; . ; 12. Divide 1 by $ ; * ; Ans. 4. Ans. 17. Ans. 5. Ans. 2. Ans. 2. Ans. 1 Ans. 2, 3, 4, 5. Ans. , , 4. Ans. 4, 6, 8, 10. Ans. f, g, 4 Ans. , , $, . 4 Ans. À |