PROBLEMS 1. A load of white oak lumber weighs 3640 lb. How many cubic feet of lumber are there in the load? how many board feet, supposing that all pieces are at least an inch thick? 2. A piece of steel is 6' 4" x 2". Find its weight. 3. Find the weight of a block of granite 4′ × 2′ × 1. 4. Find the weight of a block of ice 4′ × 2 × 10′′. 5. The ice chest of a refrigerator is 22" x 16" x 12". How many pounds of ice will it hold, allowing 2 inches in each dimension for irregularities in the ice? Suggestion. Find the weight of a regular block of ice 20" x 14" x 10". 6. What would be the weight of a cord of white pine if the wood were a solid mass? If a cord of pine weighs 2000 lb., what fraction of the space in the cord is occupied by the wood? 7. What is the weight of a white oak beam 16′ × 8′′ × 6′′? 8. What is the weight per linear foot of a cylindrical wrought iron rod, 1" in diameter? 9. What is the weight of one gallon of milk? 10. A milk can weighs 114 lb. when filled with milk and 31 lb. when empty. How many gallons does it hold? 11. A tank contains 24,640 lb. of turpentine. How many barrels, at 31 gallons each, does it contain? DRILL OF FUNDAMENTALS Copy from dictation, divide, and check. Find quotients and CHAPTER XXI PERCENTAGE 315. Percentage in Business. Next to the four fundamental operations, percentage is the most important subject in the arithmetic of business. Its manifold applications to business occupy nearly one half of this book. 316. Meaning of Per Cent. It has become customary to express a large number of fractions as hundredths, or per cents. The words per cent are derived from the Latin words per and centum, meaning "in the hundred," or "hundredths." The symbol for per cent is %. 317. Definition. - Percentage is the name used for calculations in which hundredths, or per cents, are used as the basis of comparison. 318. Base, Rate, Percentage. The principal numbers involved in percentage are the base, the rate, and the percentage. The base is the number of which a certain number of per cents, or hundredths, are taken. 66 Thus, in 5% of 200 equals 10," 200 is the base. The rate is the number of hundredths or per cents taken. Thus, in "5% of 200 equals 10," 5 per cent is the rate. The percentage is the result obtained by taking a certain per cent of a number. Thus, in “5 % of 200 equals 10," 10 is the percentage. The amount is the base plus the percentage. The difference is the base less the percentage. Per cent has come into such general use that 5% means more to the average individual than the equivalent common fraction. We even use fractional per cents. Thus, we say that 3.2% of a certain sample of milk is butter fat, while we would never say that the milk contains butter fat. 12 319. Percentage Involves only Decimal Fractions. Since percentage involves fractions whose denominators are 100, it follows that no new theory of arithmetic is involved. It will be useful, however, to gain a direct acquaintance with magnitudes represented by certain per cents. ORAL EXERCISES 1. State how many per cent of the whole figure below are shaded thus: how many per cent of the whole are shaded? How many per cent are white? How many per cent are there all together? 7. In the second little square, how many per cent are shaded? How many per cent are white? How many per cent are there all together? 8. In the third little square, how many per cent are shaded? How many per cent are white? How many per cent are there all together? 9. In the fourth little square, how many per cent are shaded? How many per cent are white? How many per cent are there all together? 10. In a class there are 16 boys and 16 girls. How many per cent of the class are girls? 320. Decimals Read as Per Cents. Since per cent means hundredths, it follows that any decimal may be read as per cent. A number of per cents such as 25% may mean .25, or of some other number, or it may simply represent .25, just as any other fraction. Example 1. Express .31 as per cent. Solution. The number of hundredths or per cent in a number is found by moving the decimal point two places to the right. 321. Reduction of Common Fractions to Per Cents. - A common fraction may be reduced to per cents by reducing it to a decimal fraction and then moving the decimal point two places to the right. |