To measure solid bodies, such as timber, wood, &c., it is necessary to use a measure that has three dimensions, length, breadth, and depth, height, or thickness. For this a measure is used in which all these dimensions are alike. Take a block, for example, and make it an inch long, an inch wide, and an inch thick, and all its corners or angles alike; this is called a solid or cubic inch; so a block made in the same way having each of its dimensions one foot, is called a solid or cubic foot. 33. If a block 1 inch wide and 1 inch thick and 1 inch long contains 1 solid inch, how many solid inches does such a block that is 2 inches long contain? 3 inches long? 4 inches long? 5 inches long? 8 inches long? 34. How many solid inches does a block that is 1 foot long, 1 inch thick, and 1 inch wide contain? How many inches does such a block that is 2 inches wide contain? 3 inches wide! 4 inches wide? 5 inches wide? 8 inches wide? 35. How many solid inches does a block 2 inches long, 2 inches wide, and 1 inch thick contain? 2 inches thick ? 36. How many solid inches does a block 4 inches long, 3 inches wide, and 1 inch thick contain? 2 inches thick? 3 inches thick ? 37. How many cubic inches in a block 10 inches long, 8 inches wide, and 1 inch thick? 2 inches thick ? 3 inches thick 5 inches thick? 7 inches thick ? 38. How many cubic inches in a block 18 inches long, 13 inches wide, and I inch thick 5 inches thick? II inches thick! In the above examples supply feet instead of inches, and do them over again. 39. What rule can you make for finding the number of solid inches or feet in any regular solid body? 40. How many solid inches in a block 12 inches long, 12 inches wide, and 12 inches thick; that is, in a solid foot? 41. A pile of wood 8 feet long, 4 feet wide, and 4 feet high, or in any other form containing an equal quantity, is called a cord of wood. How many solid feet in a cord? 42. Find the numbers for the following table. 43. How many solid inches in a cord? 1 ton or load 44. How many solid inches in a ton of hewn timber? 45. In 468,374 solid inches, how many solid feet? 46. How many feet of timber in a stick 28 feet long and 11 inches square? 47. How many tons of timber in 2 sticks, each 25 feet long, 15 inches wide, and 11 inches thick? 48. A pile of wood 4 feet square and 1 foot long, or a pile containing 16 solid feet is called 1 foot of wood. How many such feet in a cord? 49. How many solid feet of wood in a pile 5 feet wide, 3 feet high, and 23 feet long? How many feet of wood? How many cords? A few more examples of this kind will be found in decis mals. DECIMAL FRACTIONS. XXV. IN the following numbers, write the fractional part in the form of decimals. 1. Twenty-seven and six tenths, 27. Ans. 27.6. Ans. 14.07. 3. One hundred twenty-three, and eight thousandths. 123T000 Ans. 123.008. 4. One hundred and eight, and five tenths. 108. 6 6. Four, and six thousandths. 400 7. Sixteen, and one thousandth. 16. 8. Six tenths. 9. Five hundredths. 15. 10. Seven thousandths. T 11. Two ten thousandths. Toor. 2 105 12. Three, and four tenths and two hundredths. 3 and and are how many hundredths? 13. 4 are how many hundredths? 3 are how 100 are how many thousandths? 100 17.3 and 8 and 100 are how many thousandths ? 18. Write 785 in the form of a decimal. 1000 19. are how many ten-thousandths ? 5 20. are how many ten-thousandths? 00 21. 6 are how many ten-thousandths? 1000 6 22. 70, 150, 100, and 10 are how many ten-thousandths? 23. Write 2567 in the form of a decimal ? 10030 Write the fractions in the following numbers in the form of decimals. Change the decimals in the following numbers to com mon fractions and reduce them to their lowest terms. XXVI. 1. A man purchased a barrel of flour for $7.4:3. ; 5 gallons of molasses for $1.625; 3 gallons of wine for $4.87; 4 gallons of brandy for $7; 7 lbs. of sugar for $0.95; and 3 gallons of vinegar for $0.42. What did the whole amount to? 42 2. How many bushels of corn in 4 bags, the first contain. ing 2 bushels; the second, 38; the third, 3%; and the fourth, 4287 ? 1500 Note. Write the fractions in the form of decimals. 3. A man bought four loads of hay, the first containing 17 cwt.; the second, 194 cwt.; the third, 24 cwt.; and the fourth, 14 cwt. How many cwt. in the whole ? Note. In all the examples under the head of decimals, change the fractions and parts to decimals. 5 4. A man raised wheat in five fields, in the first, 47-3 bushels; in the second, 94, in the third, 871; in the fourth, 143; and in the fifth 387 bushels. How many bushels in the whole ? 5. A man bought a load of hay for 6£.; a load of oats for 7.; 3 bushels of corn for 17£.; and a load of wood for 2. How much did the whole come to? 5 20 6. Add together the following numbers, 384; 1386; 406 ; 8; and 4603. 7006; 20 97 2875 7. From a piece of cloth containing 473 yards, a mer chant sold 23. How much remained unsold? 8. A man owing $253 paid $187.375, how much did he then owe? 9. A man owing 342. paid 187. How much did he then owe? 10. A merchant sold a barrel of flour for 25£.; 5 gallons of molasses for £.; and 6 gallons of wine for 21. In pay he received a load of wood worth 2,4£. and 2 bushels of wheat, worth £. and the rest in money; how much money did he receive? 11. From 183£. take 87£. 12. From $382 take $48.25. 13. From 11534 lb. take 684-5 lb. 14. From 37 tons take 28 tons. = Multiplication of Decimals. XXVII. 1. A man bought 5 barrels of pork, at $17.43 er barrel; how much did it come to ? 2. What cost 8 yards of cloth, at $7.875 per yard? 3. How many bushels of meal in 14 sacks, containing 4.37 bushels each? 4. How much hay in 8 loads, containing 24.35 cwt. each! 5. How much cotton in 17 bales, containing 4 cwt. cach? 6. How many cwt. of hay in 14 loads, containing 23.25 cwt. each? 7. Multiply 42.62 by 38. 8. Multiply 137.583 by 17. 9. Multiply 13.946 by 58. 10. Multiply 2.5837 by 15. 11. Multiply .464 by 27. 12. Multiply .0038 by 9. 13. If a barrel of flour cost $5, what cost .6 of a barrel ? 14. At $90 per hhd., what cost .7 hhd., that is, hdd. ? 15. At $45 per hhd., what cost .8 hhd., that is, hhd. of gin? 16. At $20 per hhd., what cost 2.9 hhds., that is 2 of molasses? of a of a hhds. 17. At $25 per ton, what cost 7.6 tons of hay? 22. At $45 per thousand, what cost 2.5 thousands of Staves? 23. What is .5 of 128? 24. What is .25 of 856? 25. What is .125 of 856! 26. What is .287 of 2487 ? 27. Multiply 2487 by .287. 28. Multiply 4306 by 3.5. 29. Multiply 87 by 2.8. =30. Multiply 1864 by 3.25. 31. Multiply 30067 by 1.3873. 32. Multiply 10372 by 61-6.5. 33. Multiply 468 by 71-7.25. 34. Multiply 46800 by 133. 35. Multiply 36038 by 13. 36. Multiply 130407 by 5. 37. At .3 of a dollar a gallon, what cost .2 of a gallon of molasses? 38. What is .2 of .3, that is of ? 39. Multiply .3 by .2. 40. At $.90 per gallon, what cost .4 of a gal. of wine? 41. At $.25 per lb. what cost 2.8 lb. of butter? 42. At $.36 per lb., what cost 4.5 lb. of sperm candles? 43. At $.47 per piece, what cost 4.3 pieces of nankin? 44. At $5.37 per yard, what cost 7.4 yards of cloth? |