PRACTICAL PROBLEMS IN MULTIPLICATION OF FRACTIONS. Required the cost of Ans. $39. Ans. $0.751. Ans. $6.437. Ans. $1.20§. Ans. $5013. Ans. $24818. Ans. $565. 1. 9 yards of cloth at $4 a yard. 2. 83 quarts of nuts at 84 cts. a quart. 3. 251 yards of muslin at 25 cts. a yard. 4. 163 pounds of sugar at 74 cts. a pound. 5. 281⁄2 barrels of sugar at $173 a bar. 6. 46 cords of wood at $53 a cord. 7. 38 tons of hay at $143 a ton. 8. 53 tons of coal at $83 a ton. 9. 5 dozens of eggs at 121 cts. a dozen. 10. 963 lb. of cotton at 16 cts. a pound. 11. 85 lb. of meat at 183 cts. a pound. 12. 19 barrels of sugar at $21 a barrel. Ans. $43011. 13. What is the value of 2× 19 × 335×1378? Ans. 45. 28 90 9409 10000 17. Of (7)2×(†)3 × (?) 1 ? 18. Of (1)2 × (75) 3 × § 7 ? 3 2 Ans. $4681. Ans. $0.717. Ans. $15.95. Ans. $16.08. 19. Of (7)3× (18) 2 × (75)1× (4)5 × (51)1? Ans. 3675 20. Of (+)× 1 3 × ( 2 1 − 3 %)? 21. Of (}{+15)× (31—33)×927 × 1 9 ? 22. Of 1017—(22%−195)+163×}}? 92416* Ans. 665 864. Ans. Ans. 10917. 126 23. (161+277)—(563—493)+95×71? Ans. 715,5%. 24. When St. Louis flour is worth $63 a barrel, how much will 26 barrels cost? Ans. $1703. 25. Bought 10 dozen O. H. Swedes carpet tacks, amounting to $20.40, with a deduction first of and after of &; what was the bill? Ans. $15.60%. 26. A bill of books amounts to $5963, but I get off for wholesale and for cash; what do I pay? Ans. $373388. bought some sheep for $751, and then sold apiece, and traded the rest for half a barrel 27. A farmer 7 of them at $7 of sugar at $20 a barrel, and a barrel of mackerel at $15 a DIVISION OF FRACTIONS. 244. Division of Fractions is the process of dividing when one or both terms are fractional. 245. There are Three Cases: 1st. A fraction by an integer; 2d. An integer by a fraction; 3d. A fraction by a fraction. CASE I. 246. To divide a fraction by an integer. 1. Divide 13 by 6, also by 7. SOLUTION.- divided by one equals, hence divided by 6 equals of, which is 13; } divided by 7 equals of 13, or 1. SOLUTION 2D.-Dividing the numerator by 6, we have 6 equals (Prin. 2); multiplying the denominator by 7, we have 7 equals (Prin. 3). 2. Divide 627 by 6. 12 91 SOLUTION.-Dividing 627 by 6 we have 104 and a remainder of 3; 3 equals 12, which, added to 2, equals ; divided by 6 equals ; hence the quotient is 104ğ. OPERATION. 13÷6=1's OPERATION. OPERATION. 6)627 104ğ NOTE.-Reduce a mixed number to a fraction, or divide the integer, unite the remainder with the fraction and divide the result. 247. To divide an integer by a fraction. 1. Divide 12 by the fraction §. SOLUTION.-12 divided by one equals 12, hence 12 divided by equals 7 times 12, and 12 divided by equals of 7 times 12, which is times 12, which equals 14. Hence the following OPERATION. 12÷ = Rule I.-Multiply the dividend by the denominator of the fraction, and divide the product by the numerator. Rule II.-Invert the divisor and proceed as in multiplication of fractions. SOLUTION.- divided by one equals, hence divided by equals 6 times, and divided by equals of 6 times, which is g times, which equals. SOLUTION 2D.- equals 1, equals, and # divided by # equals 48 divided by 45, which equals or 18. OPERATION. = OPERATION. 8÷5=18÷÷35= 48451818 Rule I.-Multiply the dividend by the denominator of the divisor, and divide by the numerator. Rule II.-Invert the divisor and proceed as in multiplication of fractions. NOTES.-1. Reduce mixed numbers to simple fractions. When the divisor is a compound fraction, invert each term and multiply, cancelling when possible. 2. " Why do we invert the divisor?" The analysis requires it, or dictates it, as is shown in first solution. This reply is better than "for convenience." PRACTICAL PROBLEMS IN DIVISION OF FRACTIONS. 1. If 7 yards of cloth cost $47, what is the price per yard? Ans. $61. 2. If 18 tons of hay cost $2853, what is the price per ton? Ans. $153. 3. If 23 bags of coffee cost $410, what is the price per bag? Ans. $17. 4. If 17 barrels of sugar cost $23818, what is the price per barrel? Ans. $137. 5. If 371⁄2 tons of coal cost $253, what is the price per ton? Ans. $63. 6. If 9615 acres of land cost $676124, what is the price per acre? Ans. $693. 7. If 867 cords of wood cost $68025, what is the price per cord? 8. What is the value of 2×43 × 18 ÷ 3 ? 9. Of $99××4088-318? 561 792 720 42 1 Ans. $75. Ans.. Ans. 35. Ans. 1.403 2187 Ans. 584 Ans. 400000 407511 12. Of (21×2}+5 of 7)× (§)3÷(77—33×48) ? Ans. 1. 13. Find the value of 541-177× (64+31-2})÷ 276-815. 14. If of 3 gallons of kerosene cost of 93, what will 1 gallon cost? Ans. $. 15. The product of two numbers is 156, and one of them is 131; what is the other? Ans. 115. 16. What number is that which being multiplied by of 4 of 91, will produce 177? Ans. 217. 17. If 4 men plow 20 acres in 5 days, how much at the same rate would 6 men plow in 7 days? Ans. 4418. 18. Mr. Shaw bought 871⁄2 bushels of corn for $109g, and sold of the quantity to Mr. Landis at a profit of $2 per bushel; what did he receive for the part sold? Ans. $1163. REDUCTION OF COMPLEX FRACTIONS. 249. The Reduction of Complex Fractions is the process of changing them to simple fractions. NOTE.-A complex fraction is not really a fraction, according to the definition of a fraction. It is rather a complex fractional expression of one fraction divided by another. 1. Reduce to a simple fraction. Rule I.-Multiply the numerator of the complex fraction by its denominator inverted. Rule II. Multiply both terms of the complex fraction by the least common multiple of the denominators. |
