The pupil is required to make out a bill from the statement contained in the following example. Wm. Prentiss sold to David S. Platt 780 lbs. of pork, at 6 cents per lb.; 250 lbs. of cheese, at 8 cents per lb.; and 154 lbs. of butter, at 15 cents per lb. ; in pay he received 60 lbs. of sugar, at 10 cents per lb.; 15 gallons of molasses, at 42 cents per gallon; barrel of mackerel, $375; 4 bushels of salt, at $125 per bushel; and the balance in money: how much money did he receive? Ans. $68 85. COMPOUND NUMBERS. T102. When several abstract numbers, or several denominate numbers of the same unit value, are employed in an arithmetical calculation, they are called simple numbers, and operations with such numbers are called operations in simple numbers. Thus, if it were required to add together 7 gallons, 9 gallons, and 5 gallons, the numbers are simple numbers, being denominate numbers of the same unit value, (1 gal.,) and the operation is an addition of simple numbers. We have had, also, subtraction, multiplication, and division of simple numbers. But when several numbers of different unit values are employed to express one quantity, the whole together is called a compound number. Thus, 12 rods, 9 yards, 2 feet, 6 inches, employed to express the length of a field, is a compound num ber. So also, 9 gallons, 2 quarts, 1 pint, employed to express a quantity of water, is a compound number. NOTE. The word denomination is used in compound numbers to Questions.-T 102. What are simple numbers? Examples. What are operations in such numbers called? What is a compound number? Give examples other than those in the book. What is meant by the word denomination? denote the name of the unit considered. Thus, bushel and peck are names or denominations of measure; hour, minute and second are denominations of time. T103. The fundamental operations of addition, subtraction, multiplication and division, cannot be performed on compound numbers till we are acquainted with the method of changing numbers of one denomination to another without altering their value, which is called Reduction. Thus, we wish to add 2 bushels 3 pecks, and 3 bushels 1 peck, together. They will not make 9 bushels nor 9 pecks, (adding together the several numbers,) since some of the numbers express bushels, and some express pecks. But 2 bushels equal 8 pecks, (2 times 4 pecks, the number of pecks in a bushel,) and 3 pecks added make 11 pecks; 3 bushels equal 12 pecks, and 1 peck added make 13 pecks. Then, 11 pecks + 13 pecks 24 pecks. Hence, before proceeding further, we must attend to the Reduction of Compound Numbers. STERLING OR ENGLISH MONEY. T104. Money is expressed in different denominations, and 4 dollars, 3 dimes, 7 cents, 5 mills= $4.375, employed to express one sum in Federal money is a compound number. But as the denominations in Federal money vary uniformly in a tenfold proportion, (¶ 93,) being conformed to the Arabic notation of whole numbers, the operations in it are as in whole numbers. The denominations in English (called, also, sterling) money, pounds, shillings, pence and farthings, do not vary uniformly, but according to the following TABLE. NOTE 1. All the tables in Reduction of Compound Numbers must be carefully committed to memory by the pupil. 66 S. 4 farthings (qrs.) make 1 penny, marked d. 12 pence (plural of penny) 1 shilling, 20 shillings NOTE 2.- Farthings are often written as the fraction of a penny; thus, 1 farthing=4d., 2 farthings=4d., 3 farthings = d. 1 pound, 66 £. Questions. - 103. What is reduction? Whence its necessity? Explain by the example of adding bushels and pecks. To what, then, must we attend before proceeding further? NOTE 3.-The value of these denominations in Federal money is nearly as follows: Questions.¶ 104. What is said of operations in Federal money? What are the denominations of English money? the signs? How do they vary differently from those of Federal money? Give the table. How are farthings written? What is the value of a pound sterling in Federal money? Explain the first operation of Ex. 1; the second operation. Explain Ex. 2. Of how many kinds is reduction? what are they? What is reduction descending?-reduction ascending? The changing of higher denominations to lower, as pounds to shillings, is called Reduction Descending, and is performed by multiplication. REDUCTION DESCENDING. T105. 1. In £17 13s. 6 d., how many farthings? OPERATION. 17£ 13s. 6d. 3qrs. 20 353s. in 17£ 13s. 12 4242d. in 17£ 13s. 6d. 4 16971qrs. Ans. În 17£ 13s. 6d. 3qrs. SOLUTION. We multiply 17£ by 20. the shillings in 1£, and add in the 13s. to get the number of shillings in 17 £ 13s., which is 353. This number we multiply by 12, adding in the 6d. given, to get the number of pence, 4242, which we multiply by 4, adding in the 3qrs. given, to get the number of qrs. or farthings, which is 16971qrs. Hence, for Reduction Descending, RULE. Multiply each higher denomination by the number which it takes of the next less SOLUTION. We divide the whole number of farthings by 4, the number in 1d., to get the number of pence; for as many times as 4 can be subtracted from 16971, so many pence there will be, which is 4242d. and 3qrs. remaining. On the same principle, dividing the 4242 by 12, the quotient, 353, is shillings, and the remainder, 6, is pence, and dividing 353s. by 20, the quotient, 17, is pounds, and the remainder, 13, is shillings. Hence, for Reduction Ascending, RULE. Divide each lower denomination by the number which it takes of it to make one of Questions.¶ 105._ Explain the first example. Give the rule for reduction descending. Ex. 2. Give the rule for reduction ascending. T 106. Avoirdupois Weight is employed in all the ordinary purposes of weighing. The denominations are tons, pounds, ounces, and drams. 1 quarter, Or, as was formerly reckoned, 28 lbs. 4 qrs. (112 lbs.) By the last table, 2240 lbs. make 1 ton, which is sometimes called the "long ton;" while the ton of 2000 lbs. is called. the "short ton." The long ton is still used in the U. S. cus Questions.¶ 106. What is the use of avoirdupois weight? the denominations? the signs? Repeat the table; the table by the old method. Explain the difference between the long and short ton. When is the long ton used? the short ton? |