LESSON 105. Compound numbers can be used in every respect as simple numbers, if they are first changed to the same denomination. For the Slate. 1. A trader sold to three men the following quantities of wine to the first 2 gals. 1 qt.; to the second 3 qts. 1 pt.; and to the third 2 qts.; how much did he sell all of them? Answer, 3 gals. 2 qts. 1 pt. Explanation.-Before adding, we change all the quantities to pints, or to quarts and decimals of a quart, or to gallons and decimals of a gallon. After adding, we change them to any denomination we please. 2. Add 15 bu. 2 pks. 5 qts., 7 bu. 1 pk. 3 qts., and 23 bu. 2 pks. Answer, 46 bu. 2 pks. 3. If you are allowed to play 4 h. 20 min., how long can you remain after having played 2 h. 40 min. ? Answer, 1 h. 40min. 4. A man took 1 C. 7 ft. of wood from a heap that contained 6 C. 3 ft.; how many cords were left? Answer, 4 C. 4 ft. 5. A milkman left 2 gals. 3 qts. 1 pt. of milk at a boarding house every morning for 6 days; what quantity did he leave in that time? Answer, 17 gals. 1 qt. 6. If you have 3 loads of hay, each weighing 18 cwt. 20 lbs., how many tons have you? 3 qrs. Answer, 2 T. 16 cwt. 3 qrs. 4 lbs. 7. Multiply 33 ft. 7 in. by 4. 8. Divide 15 lbs. 9 oz. by 6. Answer, 134 ft. 4 in. Answer, 2 lb. 9 oz. 8 dr. 9. 5 men owned 1 hhd. 1 bl. 16 gals. of wine in equal shares; how much was each one's portion? Answer, 22 gals. 3,2 gi. 10. How many square feet are there in 3 carpets, each of which contains 186 sq. ft. 66 sq. in.? Answer, 559,375. It will be well to recollect that compound numbers can be used in this way, but we can add and subtract in these numbers, and can often multiply and divide them without taking the trouble to change them to the same denomination, as we shall now proceed to show. How can compound numbers be used? What else is said of them? LESSON 106. ADDITION OF COMPOUND NUMBERS. To be performed in the mind. 1. A man bought at different times the following quantities of cinnamon: 3 oz., 5 oz., and 9 oz.; how many ounces did he buy? How many pounds, &c. ? 2. How many pecks of corn will you have after harvesting 2 pks., 3 pks., and 5 pks.? How many bushels, &c., will you have? 3. A laborer worked for a merchant 4 h. 30 min. at one time, 5 h. at another, and 12 h. 30 min. at another; how many hours did he work? For the Slate. 4. A farmer sold at different times the following quantities of butter: 3 qrs. 12 lbs. 4 oz., 9 lbs. 14 oz., and qr. 15 oz.; what was the whole quantity he sold? 1 OPERATION. cwt. qrs. lbs. Oz. 3 12 4 9 14 1 0 15 1 Explanation. We first place oz. under oz., lbs. under lbs., &c. Adding up the oz. we find there are 33, or 2 lbs., 1 oz.; we place the 1 oz. under the column of oz., and add the 2 lbs. with the lbs. There not being pounds enough to make 1 qr., we write down the whole number, and then adding up the qrs., we get 4 qrs. or 1 cwt.: so we put 0 in the place of qrs. and 1 in the place of cwts. 1 0 23 Ans. 1 cwt. 0 qrs. 23 lbs. 1 oz. Therefore, to add compound numbers, Write the numbers so that the quantities in the same denomination may stand directly under each other. Add the quantities in the lowest denomination first; change the sum to the next higher denomination, and the result carry, and add with the next higher denomination, having first put down the remainder, and so on. Explain how example 4, lesson 106 of addition of compound numbers is performed. How do you add compound numbers? The work is proved as in simple numbers. 8. A farmer sold four loads of hay, weighing as follows: the first 1 T., the second 16 cwt. 2 qrs. 18 lbs., the third 1 T. 2 cwt. 10 lbs., and the fourth 18 cwt.; what was the weight of the whole? Answer, 3 T. 16 cwt. 3 qrs. 9. If I buy the following quanties of oats, 12 bu. 3 pks. 5 qts., 2 bu. 2 pks. 2 qts. 1 pt., 3 bu. 7 qts., 6 qts., and 1 pk. 4 qts., what is the whole amount purchased? Answer, 19 bu. 1 pk. 1 pt. 10. Add the following quantities of silver: 5 lbs. 11 oz. 7 pwts. 3 grs., 6 lbs., 2 lbs. 15 grs., and 20 grs. Answer, 13 lbs. 11 oz. 8 pwts. 14 grs. LESSON 107. For the Slate. 1. How much beer is there in the following quantities: 2 hhds. 1 bl., 1 hhd. 2 bls. 6 gals., and 1 bl. 3 gals.? Answer, 5 hhds, 1 bl. 1 fir. 2. The first day a ship left port, she sailed 25 lea. 2520 fath., the second day, 13 lea. 180 fath., the third day, 17 lea. 1820 fath., and the fourth day, 2 lea. 4900 fath.; how far did she sail during the four days? Answer, 60 lea. 1500 fath. Explanation.-How many feet are there in a mile? In a league? How many fathoms then are there in a league? 3. How much land is there in three pieces, the first of which contains 17 A. 3 qrs. 12 sq. rods, the second 25 A., the third, 4 A. 6 sq. rods, and the fourth, 25 sq. rods? Answer, 47 A. 3 sq. rods. How do you prove the addition ? 4. How many cords of wood are there in of a C., 2 C., 3 C. 12 ft., 1 C. 10 ft., and 13 ft.? Answer, 11 C. 4 ft. Explanation. First change of a C. to feet, and 23 C. to cords and feet. 5. A grocer sold, at different times, the following quantities of molasses: 4 hhds. 24 gals., 2 hhds. 2 bls. 4 gals. 3 qts., and 24 hhds.; what was the whole quantity sold? Answer, 30 hhds. 2 bls. 28 gals. 3 qts. 6. Add 24 y. 55 d. 17 h., 2 y. 44 d., and 5 d. 2 h. Answer, 26 y. 65 d. 1 h. 7. Add 12° 04′ 13′′, 5° 12′ 55′′, and 02′ 07′′. Answer, 17° 19′ 15." 8. There is a bin of wheat, 8 ft. square on the bottom, and 4,5 ft. high, and another bin containing 17 bu. 4 pks. 6 qts.; how much wheat is there in both bins? Answer, 249 bu. 2 pks. 3 qts. 1 pt., about. Explanation.-First find how many cubic inches of wheat there are in the first bin, and recollect that there are 2150,4 cubic inches in a bushel. 9. A man has four pieces of rope; the first is 2 yds. 2 ft. 7 in. long, the second 24 yds., the third 7 yds., and the fourth 3 yds. 1 ft. 11 in. long; what is the length of the four pieces? Answer, 38 yds. 10. A man has a farm of 120 A. 3 qrs. 21 sq. rods, and another piece of land 27 rods long, and 17 rods wide; how much land has he? Answer, 123 A. 3 qrs. LESSON 108. SUBTRACTION OF COMPOUND NUmbers. To be performed in the mind. 1. If a grocer have 12 pounds 9 ounces of butter, and sells 5 pounds 4 ounces, how much will he have left? 2. A man having a stick 2 feet 3 inches long, cut 1 foot 2 inches off from it; how long was the piece left? 3. If 1 gallon 3 quarts of wine leak out of a cask that contained 3 gallons, what quantity will be left? For the Slate. 4. A coal dealer having 212 chaldrons 4 bushels 3 pecks of coal, sold 38 chaldrons 17 bushels 2 pecks; what quantity was there left? OPERATION. chal. bu. pks. 212 4 3 38 17 2 1 Explanation. We first take the 2 pks. from 3 pks.; then, being unable to take the 17 bu. from 4 bu., we add 1 chal., or 36 bu. to 4 bu., and take 17 from 40. As. we have added 1 chal. to the greater number, to balance it, we now add 1 chal. to 38 chal. in the smaller number, and take 39 from 212. 73 23 Ans. 73 chal. 23 bu. 1 pk. Therefore, to subtract one compound number from another, Subtract the quantity in the lowest denomination of the smaller number from that above, and set down the remainder, and so on. When the quantity we are to subtract from is the smallest, add as many to it as make one of the next higher denomination, subtract, and then carry 1 to the next higher denomination of the smaller number. The work is proved as in simple numbers. Note. Each example should now be proved. 8. A trader having 215 bu. of beans, sold 38 bu. 3 pks. 4 qts.; what quantity had he left? Answer, 176 bu. 4 qts. 9. A grocer bought 4 bls. 8 gals. 2 qts. of beer, but lost 1 bl. 7 gals. 3 qts. by leakage; how much did he have left? Answer, 3 bls. 3 qts. 10. Subtract 7 lbs. 10 oz. 15 pwts. 17 grs., from 9 lbs. 11 oz. 17 pwts. 21 grs. Answer, 2 lbs. 1 oz. 2 pwts. 4 grs. Explain how you perform example 4, lesson 108. How do you subtract one compound number from another? |