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COMPOUND NUMBERS.-FEDERAL MONEY. T 25, 26 herself, who was 40 years of age when the father died; how old was the father at his death ?
Ans. 60 years 47. There is a field 20 rods long, and 8 rods wide ; how many square rods does it contain ?
Ans. 160 rods 43. What is the width of a field which is 20 rods long and contains 160 square rods?
49. What is the length of a field, 8 rods wide, and containing 160 square rods?
50. What is the width of a piece of land 25 rods long, and containing 400 square rods?
9 26. A number expressing things of the same kind is called a simple number; thus, 100 men, 56 years, 75 cents, are each of ihem simple numbers; but when a number expresses things of different kinds, it is called a compound number; thus, 43 dollars 25 cents and 3 mills, is a compound number; so 4 years 6 months and 3 days, 46 pounds 7 shillings and 6 pence, are compound numbers.
Note. Different kinds, or names, are usually called different denominations.
FEDERAL MONEY. Federal money is the coin of the United States. The kinds, or denominations, are eagles, dollars, dimes, cents, and mills. 10 mills are equal to
1 cent. 10 cents, (= 100 mills,)
= 1 dime. 10 dimes, 100 cents = 1000 mills,)
=1 dollar. 10 dollars, (= 100 dimes = 1000 cents = 10000 mills,) =1 eagle.*
Sign. This character, $, placed before a number, shows it to express federal money.
As 10 mills make a cent, 10 cents a dime, 10 dimes a dollar, &c., it is plain that the relative value of mills, cents, dimes, dollars, and eagles, corresponds to the orders of units, tens, hundreds, &c. in simple numbers. Hence, they may be read either in the loroest denomination, or partly in a higher, and partly in the lowest denomination. Thus,
34652 may be read 34652 mills; or 3465 cents and 2 mills; or, reckoning the eagles tens of dollars, and the dimes tens of cents, which is the usual practice, the whole may be read, 34 dollars 65 cents and 2 mills.
• The eagle is a gold coin, the dollar and dime are silver coins, the cent is a copper coin. The mill is only imaginary, there being no coin of that de. nomination. There are half eagles, half dollars, half dimes, and half cents, real coins.
For ease in calculating, a point (1) called a separatrix* is placed between the dollars and cents, showing that all the figures at the left hand express dollars, while the two first figures at the right hand express cents, and the third miils. Thus, the above example is written $34'652; that is, 34 dollars 65 cents iwo mills, as above. As 100 cents make a dollar, the cents may be any number from 1 to 99, often requiring tuo figures to express them for this reason, two places are appropriated to cents, at the right hand of the poini, and if the number of cents be less than ten, requiring but one figure to express them, the ten's place must be filled with a cipher. Thus, 2 dollars and 6 cents are written 2'06. 10 mills make a cent, and consequently the mills never exceed 9, and are always expressed by a single figure. Only one place, therefore, is appropriated to mills, thai is, the place immediately following cents, or the third place from the point. When there are no cents to be written, it is evident that we must write two ciphers to fill up the places of cents. Thus, 2 dollars and 7 mills are written 2'007. Six cents are written '06, and 7 mills are written '007.
Note. Sometimes 5 mills=$ cent is expressed fractionally; thus, 125 (twelve cents and five mills) is expressed 125, (twelve and a half cents.)
17 dollars and 8 mills are written, 17'008
'09 4 mills,
004 6 dollars 1 cent and 3 mills, 6'013 Write down 470 dollars 2 cents ; 342 dollars 40 cents and 2 mills; 100 dollars 1 cent and 4 mills; 1 mill; 2 mills; 3 mills; 4 mills; cent, or 5 mills;. 1 cent and 1 mill; 2 cents and 3 mills; six cents and one mill; sixty cents and one mill; four dollars and one cent; three cents; five cents; nine cents.
REDUCTION OF FEDERAL MONEY.
How many mills in one cent? in 2 cents ? in 3 cents ? in 4 cents ?
in 6 cents ? in 9 cents ? in 10 cents ? in 30 cents ? in 78 cents ? in 100 cents, (= 1 dollar)? - in 2 dollars? in 3 dollars? in 4 dollars ? in 484 cents ?
in 563 cents ? in 1 cent and 2 mills ? in 4 cents and 5 mills ? Mow many cents in 2 dollars? in 4 dollars ?
in 8 dollars? in 3 dollars and 15 cents ?
in 5 dollars and 20 cents ?
in 4 dollars and 6 cents ? How many dollars in 400 cents ? in 600 cents ?
in 280 cents ? in 40765 cents? How many cents in 1000 mills ?
• The character used for the separatrix in the "Scholar's Arithmetic” was the comma; the comma inverted is here adopted, to distinguish it from the comma used in punctuation.
How many dollars in 1000 mills? in 3000 mills ?
ir 8000 mills?
in 4378 mills ? in 846732 mills ? This changing one kind of money, doc. into another kind, without altering the value, is called REDUCTION.
As there are 10 mills in one cent, it is plain that cents are changed or reduced to mills by multiplying them by 10, that is, by merely annexing a cipher, (* 12.) 100 cents make a dollar ; therefore dollars are changed to cents by annexing 2 ciphers, and to mills by annexing 3 ciphers. Thus 16'dollars =1600 cents=16000 mills. Again, to change mills back to dollars, we have only to cut off the three right hand figures, (1 21 ;) and to change cents to dollars, cut off the two right hand figures, when all the figures to the left will be dollars, and the figures to the right, cents and mills. Reduce 34 dollars to cents.
Ans. 3400 cents. Reduce 240 dollars and 14 cents to cents. Ans. 24014 cents. Reduce $748'143 to mills.
Ans. 748143 mills. Reduce 749143 mills to dollars.
Ans. 748'143. Reduce 3467489 mills to dollars.
Ans. 3467-489. Reduce 48742 cents to dollars.
Ans. 487'42. Reduce 1234673 mills to dollars. Reduce 3469876 cents to dollars. Reduce $4867'467 to mills. Reduce 994 mills to dollars.
Ans. $ '994. Reduce 7 mills to dollars.
Ans. $ '007. Reduce $'014 to mills. Reduce 17846 cents to dollars. Reduce 984321 cents to mills. Reduce 96175 cents to dollars.
Ans. $96'17}. Reduce 2064 2 cents, 503 cents, 106 cents, 921cents, 500 cents, 7201 cents, to dollars.
Reduce 86753 mills, 96000 mills, 6042 mills, to dollars.
ADDITION AND SUBTRACTION OF FEDERAL MONEY.
1 28. From what hạs been said, it is plain that we may readily reduce any sums in federal money to the same denomination, as to cents, or mills, and add or subtract them as simple numbers. Or, what is the same thing, we may set down the sums, taking care to wrile dollars under dollars, cents under cents, and mills under mills, in such order that the separating points of the several numbers shali fall directly under each other, and add them up as simple numbers, placing the separatrix in the amount directly under the other points. What is the amount of $487'643, $132'007, $4'04, and $264ʻ102?
OPERATION. 437643 mills. 132007 mills.
4040 mills. 264102 mills.
Amount, 837792 mills, = = $ 8974792,
$ 887792 Amount.
EXAMPLES FOR PRACTICE. 1.1. Bought i barrel of flour for 6 dollars 75 cents, 10 pounds of cof: fee for 2 dollars 30 cents, 7 pounds of sugar for 92 cents, 1 pound of raisins for 123 cents, and 2 oranges for 6 cents; what was the whole amount?
Ans. $10^155. 2. A man is indebted to A, $237'62; to 6, $350; to C, $86-122 ; to D, $9'62}; and to E, $0ʻ834; what is the amount of his debts ?
Ans. $684'204. 3. A man has three notes, specifying the following sums, viz. three hundred dollars, fifty dollars sixty cents, and nine dollars eight cents; what is the amount of the three notes? Ans. $359'68.
4. Wha is the amount of $56-18, $7,374, $280, $0,287, $17, and $90'413?
5. Bought a pair of oxen for $76,50, a horse for $85, and a cow for $17-25; what was the whole amount?
6. Bought a gallon of molasses for 29 cents, a quarter of tea for 37} cents, a pound of saltpetre for 24 cents, 2 yards of broadcloth for 11 dollars, 7 yards of flannel for 1 dollar 62} cents, a skein of silk for 6 cents, and a stick of twist for 4 cents; how much for the whole ?
SUBTRACTION OF FEDERAL MONEY. 7. A man gave 4 dollars 75 cents for a pair of boots, and 2 dollars 12 cents for a pair of shoes; how much did the boots cost him more than the shoes?
2625 mills $2'625 Ans.
$2'625, Ans. 8. A man bought a cow for eighteen dollars, and sold her again for twenty-one dollars thirty-seven and a half cents; how much did he gain ?
Ans. $3'375. 9. A man bought a horse for 82 dollars, and sold him again for seventy-nine dollars seventy-five cents; did he gain or lose-and how much ?
Ans. He lost $2'25. 10. A merchant bought a piece of cloth for $176, which proving to have been damaged, he is willing to lose on it $16'50; what must he have for it?
Ans. $159'50. 11. A man sold a farm for $5400, which was $725,375 more than he gave for it; what did he give for the farm ?
12. A man having $500, lost 82 cents; how much had he left?
13. A man's income is $1200 a year, and he spends $800‘35 ; how much does he lay up?
14. Subtract half a cent from seven dollars ?
17. A man bought a barrel of flour for $6-25, 7 pounds of coffee for $1'41; he paid a ten dollar bill; how much musi he receive back in change?
MULTIPLICATION OF FEDERAL MONEY.
1 29. 1. What will 3 yards of cloth cost, at $4'62a yard ?
$4'625 are 4625 mills, which mul. $4'625
tiplied by 3, the product is 13875 mills. 13875 mills may now be re
duced to dollars by placing a point $13'875 the answer.
between the third and fourth figures,
that is, between the hundreds and thousands, which is pointing off as many places for cents and mills, in the product, as there are places of cents and mills in the sum given to be multiplied. This is evident ; for, as 1000 mills make i dollar, consequently the thousands in 13875 mills must be so many dollars. 2. At 16 cents a pound, what will 123 pounds of butter cost?
As the product of any 123, the number of pounds. two numbers will be the 16 cents, the price per pound. same, whichever of them
be made the multiplier, 738
therefore the quantity, 123
being the larger nuinber,
is made the multipli$19'68, the answer.
cand, and the price the
multiplier. 123 times 16 cents is 1968 cents, which, reduced to dollars, is $19'68.
RULE. From the foregoing examples it appears, that the multiplication of federal money does not differ from the multiplication of simple aumbers. The product will be the answer in the lowest denomination contained in the given sum, which may then be reduced to dollars.
EXAMPLES FOR PRACTICE. 3. What will 250 bushels of rye come to, at $0ʻ88£ per bushel ?
Ans. $221'25. 4. What is the value of 87 barrels of flour, at $6'37} a barrel ?
5. What will be the cost of a hogshead of molasses, containing 63 gallons, at 235 cents a gallon ?
Ans. $17'935. 6. If a man spend 125 cents a day, what will that amount to‘in a year of 365 days ? what will it amount to in 5 years ?
Ans. It will annount to $228-12} in 5 years. 7. If it cost $36'75 to clothe a soldier 1 year, how much will it cost to clothe an army of 17800 inen ?
Ans. $654150. 8. Multiply $367 by 46. 9. Multiply $0$273 hy 8600.
10. What will be the cost of 4848 yards of calico, at 25 cents, or one quarter of a dollar, per yard?
Ans. $1212. Note. As 25 cents is just d of a dollar, the operation in the ahove example may be contracted, or made shorter; for, at one dollar per yard, the cost would be as many dollars as there are yards, that is, 54848 ; and at one quarter (t) of a dollar per yard, it is plain, the