22. The following quantities of oil were used during the week: 48§ gallons on Monday; Tuesday, 52% gallons; Wednesday, 4772; Thursday, 50 gallons; Friday, 393 gallons; Saturday, 423 gallons. What was the total number of gallons used? Answer, 2801 gallons. 23. The following stores were received on board a ship: 23 tons of grate bars, 1 tons fire brick, ton of tools, ton of waste. What was their total weight? Answer, 4,7 tons. 24. Find the weight of the following: 222 pounds antimony, 199 pounds zinc, 3344 pounds copper, 4,5264 pounds iron. Answer, 5,282248 pounds. 25. A man did of a piece of work on one day, of it on the next day, of it on the next day, and completed it on the fourth day. How much of the work did he do on the fourth day? Answer, 34 105 26. In coaling ship the following amounts of coal were stored in five bunkers: 19 tons, 27 tons, 291 tons, 35 tons, and 394 tons. What was the total amount of coal stowed in these bunkers? Answer, 15112% tons. SUBTRACTION OF FRACTIONS. XX. Subtraction of fractions is the process of finding the difference between two fractional numbers. There are two cases. CASE I. XXI. When the fractions have a common denominator. 1. From subtract 2. Solution.-2 sevenths from 5 sevenths leaves 3 sevenths. Explanation: Since the denominators are the same, the numbers express parts of the same size; therefore, subtract 2 sevenths from 5 sevenths as you would subtract 2 cents from 5 cents, the remainder being in one case 3 sevenths and in the other 3 cents. RULE: From the greater numerator subtract the less; under the remainder write the denominator. XXII. When the fractions have not a common denominator. Solution.-Reducing the fractions to a common denominator, &= 38 and 37. Then 25 from 37 leaves % or 15. = 2 3 Explanation: Since the denominators are different, the numerators do not express parts of the same size; therefore, one fraction can not be subtracted from the other till they are reduced to a common denominator. RULE: Reduce the fractions to a common denominator. From the greater numerator subtract the lesser one and under the remainder write the common denominator. so borrow 1 from 3. 1 from 2 leaves 1. 18 Ans. equals can not be taken from 1 equals ; and % are %. from equals . 12. From 5 subtract. Answer, 43. 13. From 53 subtract 4. Answer, 13. 13. A piece of stock weighs 321⁄2 pounds and of a pound is taken off in turning it up in a lathe, how much will it weigh after being turned up? Answer, 31% pounds. 14. If the men in a fireroom of a ship worked 313 hours during the week in cleaning a boiler and spent the rest of the week in closing and testing it, how many hours were spent in closing and testing it, the week containing 444 working hours? Answer, 12 hours. 15. If there are 395 gallons of oil in a tank and 3 gallons were used in the starboard engine room, how many gallons were used in the port engine room if they used all of the remainder? Answer, 35% gallons. SUBTRACTION "FRACTION" EXERCISES. 1. A tank contained 253 cubic feet of oil; 15 cubic feet were pumped How many cubic feet remained? Answer, 2424. out. 3 20 2. From a bunker containing 843 tons of coal of a ton was taken for use in the bakery, 3 of a ton for use in the galley, and ton was taken from it for the steam launches. How much was left in the bunker? Answer, 8311 tons. is the value of the fraction in- 3. If 9 is added to each term of creased or diminished, and how much? 4. The diameter of a gear on the lead and the stud gear is 24 inches in diameter. their diameters? Answer, 312 inches. 5. A certain size gun in our Navy weighs 544 tons. The same size gun in the German navy weighs 483 tons. How much more does the American gun weigh than the German gun? Answer, 53 tons. 6. The diameter of a piece of work at one end is 33 inches and the diameter at the other end is 23 inches. What is the difference in the diameters? Answer, inch. 5 7. The area of a steam piston on one side is 4793 inches, the area of the other side is 473 inches. (The decrease in area is due to the cross sectional area of the piston rod.) How much more area has one side than the other? Answer, 624 inches. MULTIPLICATION OF FRACTIONS. XXIII. Multiplication of fractions is the process of finding the product of two or more fractional numbers. 1. If 1 apple cost of a cent, what will 3 apples cost? Solution. They will cost 3 times of a cent, or 12 of a cent. Explanation: 3 apples will cost 12 equals 23. times equals 12. ++=12 of a cent. Hence, 3 2. At 12 cents per yard, what will of a yard of canvas cost? Solution. times 12, or 24. of a yard will cost of 12, or 12. Then will cost 2 24 equals 4. 3. What will of a yard of canvas cost at of a dollar per yard? Solution. is the same as of 4. multiplied by 4 is . Then multiplied by 3 of 4 is of, or 1o. 8 RULE. Multiply together the numerators of the given fractions for the numerator of the product. Multiply together the denominators of the given fractions for the denominator of the product. NOTE.-Express integers in the form of a fraction. Reduce mixed numbers to improper fractions. Sometimes it may be more convenient to multiply by the integral and fractional parts separately. Indicate the operation and apply the rule for cancellation wherever it is practicable. 5. Multiply by 3. 6. Multiply 8 by . 7. Multiply by . 8. Multiply by 4. Answer, 21. 15 28 Solution. Indicating the operation and applying the rule for cancellation, the result is . Solution.-Reducing 24 and 3 to improper fractions they are and. Multiplying together and the result is 3 or 7. 17. Multiply 18 by 8. 183 8 144 6 150 Answer, 293. Solution.-8 times 18 are 144. 8 times are 6. 144 plus 6 equals 150. 18. Multiply 8 by 33. 19. Multiply 2 by 2. 20. Multiply 103 by 7. 21. Multiply 25 by 83. 22. Multiply by 17. 23. Multiply 108 by 9. 24. Multiply 64 by 83. 25. Multiply 8 by . Multiply together26. 12, 16, 21. 27. 216, 11, 13. 28. 64, 28, 21. 5 3 Answer, 15. 5 Answer, 48. 29. 21, 23, 44, 14. Answer, 3641. 30. 21, 2, 34, 15. Answer, 22. XXIV. Fractional parts of integers are obtained by multiplication. . Then 3 of 2 is 2 times or . equals 13. Answer, 34. Answer, 24. XXV. Compound fractions are reduced to simple fractions by multiplication. 1. Reduce of to a simple fraction. Solution. Multiplying X = 15. by the result is 15. Answer, 10. 33 2. Reduce of to a simple fraction. 5. Reduce 11 Answer, 3. MISCELLANEOUS EXAMPLES. What will be the cost 1. Of 2 cents. 2. Of 3 pounds of packing, at 133 cents per pound? Answer, 30 pounds of bolts, at 43 cents per pound? Answer, 16 cents. tons of iron, at $18 per ton? Answer, $60. 3. Of 3 4. Of 1 yards of toweling for grease extractors, at $2 per yard? Answer, $1. 5. Of 25 pounds of graphite, at $3 per pound? Answer, $2. 6. At the rate of 5 miles per hour, how far will a steam launch travel in 7 hours? Answer, 423 miles. 7. I own of a steamboat and sell of my share. the boat do I sell? Answer, . What part of 8. At $6 per ton, what will be the cost of of a load of coal containing 5 tons? Answer, $84. Answer, 343. Answ r, 111. 9. 3 of 5 of 16 × off 15? 10. What is the sum of + and × 2? 11. If there were 923 feet of grate surface in a boiler and 93 pounds of coal were burned per square foot of grate surface, per hour, what amount of coal would be burned in 24 hours? Answer, 21,460 pounds. 12. If 43 pounds of water was evaporated per pound of coal, in the above example, how many pounds of water were evaporated? Answer, 92,993 pounds. 13. A vessel makes, on an average, 10 knots per hour. How many knots will she make in 761⁄2 hours? Answer, 790 knots. 14. A piece of work tapers of an inch in 1 inch. taper in 6 inches? Answer, inch. DIVISION OF FRACTIONS. What will it XXVI. Division of fractions is the process of finding the quotient of two fractional numbers. 1. If 3 yards of manila line cost & dollars, what will 1 yard cost? |