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he is charged with 126 pounds of beef at 9 cents per pound; 85 pounds of veal at 6 cents per pound; 6 pairs of fowls at 37 cents a pair; and 3 hams at $1,50 each: how much does he owe him?

Ans. $23, 16. 6. A farmer agrees to furnish a merchant 40 bushels of rye at 62 cents per bushel, and to take his

pay in coffee at 16 cents a pound : how much coffee will he receive ?

Ans. 155 pounds. 7. A farmer bargains with his tailor for a new coat every six months,a new vest every three months, and three pairs of pantaloons a year: the coats to cost $29, 50 each, the vests 3 dollars a piece, and the pantaloons $12 a pair: at the end of two years how much did he owe him?

Ans. $214.

New-York, May 1st, 1832. Mr. James Spendthrift

Bought of Benj. Saveall 16 pounds of tea at 85 cents per pound.

27 pounds of coffee at 15} cents per pound. | 15 yards of linen at 66 cents per yard.

$27, 68, 6. Rec'd payment,

Benj. Saveall.

Albany, June 2d, 1832. Mr. Jacob Johns Bought of Gideon Gould 36 pounds of sugar at 91 cents per pound. 3 hogsheads of molasses, 63 galls. each at

27 cents a gallon. 5 casks of rice 285 pounds each, at 5 cts. per pound. 2 chests of tea 86 pounds each, at 96 cts. per pound.

Total cost $290,82 For Gideon Gould,

Charles Clark

}

Rec'd payment,

OF DENOMINATE NUMBERS. $ 70. Simple numbers express a collection of units of the same kind, without expressing the particular value of the unit. For example, 40 and 55 are simple numbers, and the unit is 1, but it is not expressed whether the unit is 1 apple, 1 pound, or 1 horse.

$ 71. A denominate number expresses the kind of unit which is considered. For example, 6 yards of cloth is a denominate number, the unit, 1 yard of cloth, being denominated, or named.

$ 72. When two numbers have the same unit, they are said to be of the same denomination: and when two numbers have different units, they are said to be of different denominations.

For example, 8 feet and 10 feet are of the same denomination, the unit being 1 foot; but 30 feet and 60 yards are of different denominations, the unit of the first being 1 foot, and the unit of the second, 1 yard.

Several denominate numbers, of different denomi. nations, are often connected together, forming a whole; as 3 feet 6 inches; 9 dollars 6 dimes and 7 cents. In the first, 1 foot is the unit of 3 feet, and 1 inch, the unit of 6 inches; and in the second, 1 dole lar is the unit of 9 dollars, 1 dime the unit of 6 dimes, and 1 cent the unit of 7 cents.

The following Tables show the different kinds of denominate numbers in general use, and also their relative values.

ENGLISH MONEY. 673. The denominations of English Money, are neas, pounds, shillings, pence, and farthings.

12 pence

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TABLE. 4 farthings marked far. make 1 penny marked d.

1 shilling 20 shillings

1 pound 21 shillings

1 guinea £

d far.
1 = 20 240 960

12 = 48
1 4

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Note.--Farthings are generally expressed in fractions of a penny. Thus, for 1 farthing we write Id, for 2 farthings, fd, and for 3 farthings, id.

QUESTIONS. $ 70. What are simple numbers ? What is the unit? Is its value expressed ?

g 71. What is a denominate number?

$ 72. When are two numbers of the same denomination ? When of different denominations ? Are numbers of differont denominations often connected together? Give an example.

$ 73. What are the denominations of English Money? Re. peat the table. How are farthings generally expressed ?

REDUCTION OF DENOMINATE

NUMBERS. $ 74. Reduction is changing the denomination of a number without altering its value.

For example, 42 dollars and 35 cents are express. ed in different denominations. But 42 dollars are equal to 4200 cents, $ 63.

Add

35 cents,

The sum 4235 cents is ec 42 dollars and 35 cents. Here we have brou

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numbers to the same denomination without altering their value.

Again, if we have 24 shillings, we can reduce them to pounds and shillings, for, since 20 shillings make 1 pound, 24 shillings are equal to £1 4s. Here we have again changed the denomination without altering the value.

$75. Reduction then is divided into two parts.

1st. To reduce a number from a higher denomination to a lower.

2d. To reduce a number from a lower denomination to a higher.

CASE I. $ 76. To reduce denominate numbers from a higher denomination to a lower.

RULE. I. Consider how many units of the next lower denomination make one unit of the higher.

II. Multiply the higher denomination by that number, and add to the product the number belonging to the lower: We shall then have the equivalent num. ber in the next lower denomination.

III. Proceed in a similar way through all the denominations to the last ; the last sum will be the required number.

Ex. 1. Reduce 25 Eagles 8 dollars 65 dimes and 35 cents, to the denomination of cents.

25 Eagles the highest denomination.

10 dollars make one eagle. 250 Product in dollars.

8 the number in the denomination of dolls.

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250

ber of dimes in a dollar.
in dimes.

2580 Product in dimes.

65 the number in the denomination of dimes. 2645

10 number of cents in a dime. 26450 Product in cents.

35 cents to be added. 26485 Number of cents in 25 Eagles, 88, 65 dimes

and 35 cents. 2. Reduce £27 6s 8d to the denomination of pence.

In reducing, we often add the next £27 6s 84 lower denomination, mentally, with. 20 out setting it down. In this exam. 640 ple, when we multiply by 20, we could 68 have added the 6s, without writing it

5468 down, making 6 in the product, in the

12 units place: and when we multiplied by 12 we might have said, 12 times 6

6552 are 72 and 8d to be added make 80.

8d The number of pence in the given

65602 denominate number is 6560.

CASE II. ģ 77. To reduce denominate numbers from a low. er denomination to a higher.

RULE. 1. Consider how many units of the given denomi. nation make one unit of the next higher; and tuke this number for a divisor : divide the given number by it and set down the remainder, if there be any.

II. Divide the quotient thus obtained by the num. ber of units in the next higher denomination, and set doron the remainder.

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