O. B. Hopkins & Co. No. 4.-Bill of goods sold at wholesale. Rec'd payment, by note, at 60 days. For Barnes Porter & Co. James D. Willard. It is sometimes practised, in collecting and settling accounts to make a copy of each individual account, and present it to. the person for his inspection. 1847. No. 5.- Copy of an individual account. Jan. 7. To 125 bushels corn, In acc't with Edward F. Cooper, Dr. Questions. 101. What is a bill? If the amount of the bill be paid at the time, how is it shown? Which oil is an example of this? if charged in account, how is it shown? example? How does a barter bill differ from a bill of sale? In what order are the articles bought and sold arranged? What is practised in collecting and settling accounts? How does such a copy differ from a barter bill? To which of the bills must the bill to be made out conform? and what will it be called? Baltimore, May 9th, 1847. Amount due me, $16,42 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 number. 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 do ominations of measure; hour, minute and second are denominations of time. ¶ 103. 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, (T93,) 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 NOTE 1.. TABLE. All the tables in Reduction of Compound Number must be carefully committed to memory by the pupil. 66 4 farthings (qrs.) make 1 penny, marked d. 1 pound, S. 66 £. NOTE 2.- Farthings are often written as the fraction of a penny, thus, I farthing =4d., 2 farthings d., 3 farthings=d. = 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? SOLUTION.We divide th 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 |