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bers, giving the name of the lowest denomination, or right hand figure to the whole. Thus ,52 is read 52 hundredths ,425 is read 425 thousandths, &c.

11. When whole numbers and decimals are expressed in the same number, it is called a mixed number.

Write, in decimals, the following mixed numbers.
1. Twenty-five and six tenths=25,6.
2. Sixteen, and seventy-five hundredths.

3. Forty-one, and one hundred and forty-five thousandths.

4. 362, and nine millionths.
5. Nineteen, and 34756 hundred thousandths.
6. 794, and twenty-five ten thousandths.

10% ; 56,86%; 411500 ; 95100%; 1451060000, &c.

ADDITION OF DECIMALS.

RULE.

1. Place the numbers, whether mixed or pure decimals, under each other, according to the value of their places.

2. Add them together as whole numbers, and place the separatrix exactly under the separating point above.

EXAMPLES,

1. What is the sum of 28,753 ; 365,41 ; 18,75 ; 145,6. 28,753

We place tenths under tenths, hund365 ,41 redths under hundredths, &c., accord

18,75 ing to the value of their places, and 145,6

add the columns as whole numbers;

and the amount is 55.8 units, and 513 558 ,513 thousandths of a unit. Note. We may here observe, that the denominations of Federal Money correspond exactly with decimals, the del: lars being units, dimes being tenths,.cents hundredths, and mills thousandths of dollars, &c.

2. Add together the following sums of dollars and decimals of a dollar, viz : 13,755, 2,50, 25,3, and 41,144.

Ans. $82,699=82dols. 6.9cts. 9m. 3. Find the amount of 79,45dols., 36,045dols., 128,5 dols., 95,006dols., 135,25dols., and 14,146dols.

Ans. 488dols. 39cts. 7m.

4. Add together the following mixed numbers, viz: 5,98471 +18,568+2,005+9,15+35,1009+,35762.

Ans. 71,16623. 5. What is the whole sum of 5,91 acres, 3,5 acres, 8,596 acres, ,795 acres, and 14 acres ? Ans. 32,801 acres.

6. Required the sum of 25,164lbs., 9,56lbs., 87,31lbs., 256,25lbs., 9,18lbs., and 125,9lbs. Ans. 513,364lbs. 7. Add together 276, 54,321, ,65, 112, 12,5 and ,0463.

Ans. 455,5173 8. What is the sum of 51 ounces; 7.1966 ounces, 31.60 ounces, 1516 ounces and 2516 ounces?

Ans. 56,985. 9. Find the amount of forty-five hundredths, two hundred and fifty-six thousandths, sixty-five hundredths, ten, and six hundred and forty-four thousandths.

Ans. 12.

SUBTRACTION OF DECIMALS.

RULE.

Place the numbers according to their value, then subtract as in whole numbers, and point off the decimals as in addition of decimals.

EXAMPLES.

1. From 215,64

2. From 95,3465
Subtract 141,56875

Take 14,04
Remains 74,07125

81,3065 3. From 356 take 198,5693.

Ans. 157,4307. 4. From $51,978 take $25,36. Ans: $26,618. 5. From 480, take 245,0075.

234,9925. 6. From 295 subtract 201,9.

Ans. 93,1. 7. From 319, take ,9125.

Ans. 318,0875. 8. From 35000, take ,035.

Ans. 34999,965. 9. From 271, take 213,95.

Ans. 57,05. io. From 10, subtract one millionth part of a unit.

Ans. 9,999999

Ans.

MULTIPLICATION OF DECIMALS.

RULE. Multiply as in whole numbers, and point off as many figures in the product for decimals, as there are decimal

places in both factors. If the number of figures in the product be less than the decimal places in both factors, prefix ciphers to the left to supply the defect.

EXAMPLES.

1. Multiply 75 by ,8. Operation.

Multiplying by a fraction is taking a 75

certain part of the multiplicand for the ,8

product : consequently, multiplying &

whole number by a certain part of a Ans. = 60,0

whole number, as 8 tenths, produces a product less than the whole number : in this example, the number of decimal places in the factors being one, therefore we point off one figure in the product, and the atiswer is 60. Likewise multiplying onie decimal fraction by another, produces a fraction smaller than either of the factors. 2 Multiply 4,25 by 3,6.

3,6 In this example, the whole number 2550 of decimal places in both multipliet

1275 and multiplicand is three, therefore Ans. 15,300

we point off three figures in the

product. 3. Multiply 5,34 by ,008.

,008 In this example, the number of ,04272 figures in the product is less than

the decimal places in both factors ; the defect must be supplied by prefixing a cipher ; that is, placing it at the left hand. 4. Multiply 36,5 by 7,27.

Ans. 265,355. 5. Multiply 3,92 by 196.

Ans. 768,32. 6. Multiply 29,831 by ,952.

Ans. 28,399112. 7. Multiply 79,347 by 23,15. Ans. 1836,88305: 8. Multiply ,009 by ,009.

Ans. ,000081. 9. Multiply 25 dollars by 25 cents, and what is the product ?

Ans. $6,25. 10. What cost 8,75 yards of cloth, at $3,96 per yard ?

Ans. $34,65. 11. What cost 18,75 barrels of flour, at $6,75 per barrel ?

Ans. $126, 56c. 2 jom. 12. What is the value of 18,25lbs. of butter, at $ , 125 per pound ?

Ans. $2 28c. 1, om.

13. At ,03cts. profit on a dollar, what is the profit on $18,75?

Ans. 56cts. 26 m. 14. Multiply 135 dollars by $ ,06 or cents. Ans. $8,10. 15. Multiply $14,56 by $1,25.

Ans. $18,20. 16. Multiply 3672 by ,85.

Ans. 3121,2. 17. Multiply 235,45 dollars by ,007, or 7 mills.

Ans. Idol. 64cts. 816.m. 18. Multiply $ ,95 or 95cts, by $ ,125, or 12cts. 5m.

Ans. 11cts. 816.m. 19. How much is ,5 of 138.

Ans. 69. 20. How much is 6 per cent, or ,06 of $1495 ?

Ans. $89,70. Note. To multiply by 10, 100, 1000, &c., remove the decimal point as many places to the right as the multiplier has ciphers.

multiplied by 10 is 3,65 Thus, ,365

100

is 36,5 1000 is 365.

DIVISION OF DECIMALS. Division of decimals differs from the division of whole numbers only in pointing off the decimal places. We have seen, in Multiplication of decimals, that the decimal places in the product must be equal to the number of decimal places in both factors counted together. So in division of decimals, the number of decimal places in the divisor and quotient counted together, must be equal to the number of decimal places in the dividend ; because the divisor and quotient are the factors which produce the dividend.

RULE.

1. Divide as in whole numbers, and from the right hand in the quotient point off as many figures for decimals, as the decimal places in the dividend exceed those in the divisor.

2. If the places in the quotient be not so many as the rule requires, supply the deficiency by prefixing ciphers.

3. If the divisor has more decimal places than the dividend, annex as many ciphers as you please to the dividend so as to make it equal at least to the divisor. also annex ciphers to the remainder, if any, and carry on the

You may

quotient to any degree of exactness; but the ciphers annexed must be counted as so many decimals of the dividend.

EXAMPLES.

1. Divide 89,756 by ,8. ,8)89,7560

We divide as in whole numbers,

and there being a remainder, we an112,195

nex a cipher and divide : there are now four decimal places in the dividend and one in the divisor. We therefore, by the rule, point off three figures in the quotient for decimals, which makes the number of decimal places in the divisor and quotient counted together; equal to the number of decimal places in the dividend. 2. Divide ,36792 by 4,2. 4,2),36792(,0876 In this example, there are five 336

decimal places in the dividend, and 319

only one in the divisor ; therefore 294

we must point off four figures in the

quotient. Now, because there are 252

only three figures in the quotient; 252

we place a cipher on the left, and 0

the decimal places in the divisor and quotient counted together, are equal to the decimal places in the dividend. 3. Divide 44,98 by 1,3.

Ans. 34,6. 4. Divide 14, by ,7854.

Ans. 17,825. 5. Divide 6,9564 by 856.

Ans. ,00812 Xi 6. Divide ,009564 by ,008.

Ans. 1,1955. 7. Divide ,07646 by 246.

Ans. ,00031 X 8. Divide 16 by 248.

Ans. ,0645 X 9. Divide $256,125 by 12,5.

Ans. $20,49. 10. Divide $510, by $1256.

Ans. $,40605 X 11. If 8,75 yards of cloth cost $34,65, what is that a yard ?

Ans. $3,96. 12. Bought 18,75 barrels of flour for $126,5625; how much was that a barrel ?

Ans. $6,75cts. 13. If 148,5lbs. of butter cost $18,5625, what will ilb. cost ?

Ans. $ ,125=12£cts. 14. At $1,79 per barrel, how many barrels of cider can be bought for $270,29 ?

Ans. 151. 15. If a bushel of wheat cost $1,87, how many bushels can be bought for $28,985 ? Ans. 15,5bu. 151bu.

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