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OPERATION.

9425

3.25

47125

18850 28275

$30631.25

This value of $30631-25 is evidently 1000 times too much; therefore, to obtain the true value, we must divide it by 1000, which is done, (ART. 57,) by removing the decimal point three places to the left; it will then become $30-63125. Had they been $3.25 per 100, then, instead of removing the decimal point three places to the left, we should have

removed it two places. Hence we have this

RULE.

Multiply the number of articles by the number expressing the price per 100, or 1000, and from the product cut off two of the right-hand figures when the articles are estimated by the 100, and three when they are estimated by the 1000.

EXAMPLES.

1. What is the value of 1300 feet of hemlock boards, at $5.50 per 1000?

OPERATION.

1300

5.50

65000

65

$7.15000

In this product we set off five figures for decimals; two according to ART. 52, and three more because the articles are estimated by the 1000.

2. What is the value of 675 feet of clear pine stuff, at $25 per 1000? Ans. $16.875.

3. What is the value of 11035 feet of timber, at $2.25 per 100? Ans. $248.2875. 4. What is the value of 90422 brick, at $3.75 per 1000? Ans. $339.0825.

5. What must be paid for laying 875 brick, at $3.25 per 1000? Ans. $2.84375. 6. A compositor worked nine months, and during that time set up at the rate of 7000 m's per day. How many thousand m's did he set up, reckoning 25 working days to the month? and how much did he receive at 15 cents per 1000 m's? Ans. 1575 thousand m's.

$236.25 amount he received. 7. Add together the following fractional parts of a dollar, ta, fo, t, t, b, d,, (See Table under ART. 61.) Ans. $1.87

89

8. A man in balancing his family accounts for one year, found his expenses as follows: for January, $98·41; for February, $8133; for March, $102.28; for April, $125.26; for May, $74-38; for June, $73-47; for July, $65.98; for August, $87-21; for September, $70-34; for October, $122.08; for November, $79-68; for December, $52.77. His salary was $1050 per annum. What had he left at the end of the year? Ans. $16.81.

9. A butcher, a shoemaker, and a tailor gave orders on each other in the way of their business, and at the end of a year settled accounts. The butcher's bill against the tailor was $61-84; against the shoemaker, $39.44. The shoemaker's bill against the butcher was $24 30; against the tailor, $19.15. The tailor's bill against the butcher

was $42-07; against the shoemaker, $39 39. received balances in cash?

Who

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NOTE.-By an Act of Congress passed Feb. 20, 1849, the Double Eagle and the Gold Dollar were added to the Gold Coins of the United States. The act directing the coinage of these pieces is to be in force until March 4, 1851. See Art. 58.

DENOMINATE NUMBERS.

64. A SIMPLE NUMBER is an expression for a certain number of units having no reference to particular things. Thus 37 is the same as 37 times one, abstractly considered; that is, considered apart from anything that units might represent. It does not mean 37 times a pound, foot, dollar, or anything else.

A DENOMINATE NUMBER is an expression for a certain number of units having reference to particular things. It denominates what things are meant. Thus 8 yards is a denominate number whose unit is 1 yard; 8 dollars is a denominate number whose unit is one dollar.

Several numbers of different denominations are frequently grouped together, as 6 feet 3 inches.

are

All our different kinds of weights and measures denominate numbers. It is much to be regretted that we are obliged to employ such a variety of different measures, when the same end would be accomplished by one measure for weight, and one for each of the three geometrical magnitudes, lengths, surfaces and solids,and one for time

The French government have adopted such a system of weights and measures, graduated on the decimal scale of notation.

In multiplication, the multiplicand being repeated a certain number of times, or a certain fraction of a time, when the multiplier is a fraction, it follows that the multiplier, considered as a multiplier, must always be regarded as a simple or abstract number. And since the product is a repetition of the multiplicand, it must be like the multiplicand; that is, if the multiplicand is an abstract number, the product will be an abstract number; if the multiplicand is a denominate number, the product will be a denominate number of the same kind.

In division, the quotient showing how many times the divisor is contained in the dividend, or what fraction of a time when the divisor is greater than the dividend, it follows that the quotient must be regarded as an abstract number; and that the divisor and dividend must be alike.

NOTE. In many cases, however, the process of division is rather the dividing of a dividend into as many equal parts as are indicated by the divisor; in which case, the quotient, expressing the units in one of those parts, is of the same kind as the dividend, while the divisor is to be regarded as an abstract number. See Example, ART. 86.

What is a simple number? What is a denominate number? What kind of numbers are all our different weights and measures? What is said of the French measures? In multiplication, can the multiplier ever be a denominate number? Are the product and multiplicand always alike? What is said of the quotient? What is said in the note?

The following are some of the most important tables of weights and measures at present employed in this country.

ENGLISH MONEY.

65. The denomination of English money are Farthings, Pence, Shillings, and Pounds.

The pound sterling, which was not a coin, but a bank

note of 20 shillings, has now gone into disuse, and a gold coin, called a Sovereign, supplies its place; but the name pound is still given to 20 shillings.

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NOTE.-Farthings are sometimes expressed in fractions of a penny, as follows: 1 farthing=4 d., 2 farthings=d., 3 farthings = d.

What are the denominations of English money? Which denomination is never coined? What gold coin is equivalent in value to one pound? Repeat the Table. How are farthings sometimes expressed?

TROY WEIGHT.

66. The original of all weights used in England was a grain or corn of wheat, gathered out of the middle of the ear; 32 of these, well dried, were to make one pennyweight, 20 pennyweights one ounce, and 12 ounces one pound. But in latter times, it was thought sufficient to divide the same pennyweight into 24 equal parts, still called grains, being the least weight now in common

use.

Coins, precious metals, jewels, and liquors, are weighed by Troy weight.

* The full weight and value of English gold and silver coin are as in the succeeding table, note.

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