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13. Bought of L. Johnson 7fyds. of broadcloth, at $ 37 per yard, and sold it at $4$ per yard; what was gained?
Ans. $ 3.68% 14. Bought a piece of land, that was 47* rods in length, and 2916 in breadth ; and from this land, there was sold to Abijah Atwood 5 square rods, and to Hazen Webster a piece that was 5 rods square ; how much remains unsold ?
Ans. 136683 square rods. 15. Bought a tract of land that was 97 rods long and 4814 rods wide ; and from this I sold to John Ayer, a houselot, 18 rods long, and 143 rods wide ; and the remainder of my purchase was sold to John Morse, at $ 3.75 per square rod ; what sum shall I receive ?
Ans. $ 16717.3013. 16. What are the contents of a box 8 feet long, 5 feet wide, and 3 feet high?
Ans. 120 solid feet. 17. What are the contents of 10 boxes, each of which is 7 feet long, 47 feet wide, and 3 feet high ?
Ans. 1312 4 feet. 18. Polly Brown has $ 17.874 ; half of this sum was given to the missionary society, and of the remainder she gave to the Bible society ; what sum has she left ?
Ans. $3.571. 19. What number shall be taken from 125, and the remainder multiplied by 10 that the product shall be 50 ?
Ans. 8715 20. What number must be multiplied by 73, that the product may be 20 ?
Ans. 245. 21. Bought of John Dow 97 yards of cloth at $4.62
per yard; what was the whole cost? Ans. $ 45.67 22. Bought of John Appleton 47 gallons of molasses
for $ 12.371 ; what cost one gallon ? what cost 127 gallons ?
Ans. $ 3.33 11 23. When $ 15.874 are paid for 123 bushels of wheat, what cost one bushel ? what cost 11 bushels ?
Ans. $ 14.115. 24. When $ 19.184 are paid for 3 cords of wood, what cost one cord ? what cost of a cord ?
Answer to the last, $2 1336 25. What are the contents of a box 811 feet long, 311 feet wide, and 21 feet high? Ans. 68117 feet.
A Decimal Fraction is that, whose integer is always divided into 10, 100, 1000, &c. equal parts. Its denominator is always an unit, with as many ciphers annexed, as there are places in the given decimal. There is, therefore, no need of having the denominator expressed ; for the value of the fraction is always known by placing a point before it, at the left hand, called the separatrix. Thus, .5 is %,.37 is 15, .348 is 1346.
Ciphers annexed to the right hand of decimals do not increase their value ; for .4 or .40 or .400 are decimals having the same value, each being equal to X or ; but when ciphers are placed on the left hand of a decimal, they decrease the value in a tenfold proportion. Thus .4 is to, or four tenths ; but .04 is to, or four hundredths; and .004 is
Tocy, or four thousandths. The figure next the separatrix is reckoned so many tenths ; the next at the right, so many hundredths; the third is so many thousandths; and so on, as may be seen by the following
From this table it is evident, that in decimals, as well. as in whole numbers, each figure takes its value by its distance from the place of units.
Note. If there be one figure in the decimal, it is so many tenths ; if there be two figures, they express so many hundredths; if there be three figures, they are so many thousandths, &c.
NUMERATION OF DECIMAL FRACTIONS.
Let the pupil write the following numbers. 1. Three hundred seven, twenty-five hundredths. 2. Forty-seven, and seven tenths. 3. Eighteen and five hundredths. 4. Twenty-nine and three thousandths. 5. Forty-nine ten thousandths. 6. Eight and eight millionths. 7. Seventy-five and nine tenths. 8. Two thousand and two thousandths. 9. Eighteen and eighteen thousandths. 10. Five hundred five, and one thousand six millionths.
ADDITION OF DECIMALS.
1. Add together 5.018 ; 171,16 ; 88.133; 1113.6 ; .00456, and 14.178. OPERATION.
5.018 =Five and eighteen thousandths. 171.16 = One hundred seventy-one, sixteen hundredths. 88.133
= Eighty-eight, and one hundred thirty-three thousandths, 1113.6
= One thousand one hundred thirteen, and six tenths.
= Fourteen, and one hundred seventy-eight thousandths. 139 2.0 935 6 =
One thousand three hundred ninety-two, and nine
thousand three hundred fifty-six hundred thousandths.
Write the numbers under each other according to their value, add as in whole numbers, and point of from the right hand as many places for decimals, as there are in that number, which contains the greatest number of decimals.
2. Add together 171.61111 ; 16.7101 ; .00007; 71.0006, and 1.167895.
Ans. 260.489775. 3. Add together .16711 ; 1.766 ; 76111.1; 167.1 ; .000007, and 1476.1.
Ans. 77756.233117. 4. Add together 151.01 ; 611111.01 ; 16.5 ; 6.7 ; 46.1, and .67896.
Ans. 611331.99896. 5. Add fifty-six thousand and fourteen thousandths, nineteen and nineteen hundredths, fifty-seven and forty-eight ten thousandths, twenty-three thousand and five and four tenths, and fourteen millionths. Ans. 79081.608814. 6. What is the sum of forty-nine and one hundred and five ten thousandths, eighty-nine and one hundred seven thousandths, one hundred and twenty-seven millionths, forty-eight ten thousandths ? Ans. 138.122427. 7. What is the sum of three and eighteen ten thousandths, one thousand five and twenty-three thousand forty-three millionths, eighty-seven and one hundred seven thousandths, forty-nine ten thousandths, and forty-seven thousand and three hundred nine hundred thousandths ?
SUBTRACTION OF DECIMALS.
Let the numbers be so written that the separatrix of the subtrahend be directly under that of the minuend, that is, units under units, and tens under tens, f-c.; subtract as in whole numbers, and point off so many places for decimals, as there are in that number, which contains the greatest number of decimals.
4. 1 1.078 47.1 17
87.1 07 9.8 1
8.7 8195 7.8915 1.1 1986
38.3 35 0 5
5. From 81.35 take 11.678956. Ans. 69.671044. 6. From 1. take .876543.
Ans. .123457. 7. From 100. take 99.111176.
Ans. .888824. 8. From 87.1 take 5.6789.
Ans. 81.4211. 9. From 100. take .001.
Ans. 99.999. 10. From seventy-three take seventy-three thousandths.
Ans. 72.927. 11. From three hundred sixty-five take forty-seven ten thousandths.
Ans. 364.9953. 12. From three hundred fifty-seven thousand take twentyeight and four thousand nine ten millionths.
Ans. 356971.9995991. 13. From .875 take .4.
Ans. .475. 14. From .3125 take .125.
Ans. .1875. 15. From .95 take .44.
Ans. .51. 16. From 3.7 take 1.8.
Ans. 1.9. 17. From 8.125 take 2.6875.
Ans. 5.4:375. 18. From 9.375 take 1.5.
Ans. 7.875. 19. From .666 take .041.
MULTIPLICATION OF DECIMALS.
1. Multiply 18.72 by 7.1.
Ans. 132.912. OPERATION BY DECIMALS.
BY VULGAR FRACTIONS,
181% = 1072
102 xH1=143812=1329,1% Ans. 2. Multiply 15.12 by .012.