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25. What is the amount of $391.00 from 1834, Jan. 15, to 1842, Aug. 9, (1834Y. 1mo. 15dy. to 1842Y. 8mo. 9dy.,) at 6 per cent.?

26. What is the amount of $1250.00 from Feb. 7, 1836 to Jan. 1, 1844, at 6 per cent.?

27. What is the amount of $6250.00 from Oct. 13, 1835 to May 29, 1841, at 6 per cent. ?

28. What is the interest of $8750.00 from March 20, 1839 to June 3, 1844, at 6 per cent.?

29. What is the interest of $5599.00 from Aug. 29, 1837 to July 13, 1843, at 6 per cent.?

30. What is the amount of $7001.50 from Sept. 16, 1829 to Nov. 2, 1842, at 6 per cent. ?

EXAMPLE FOR THE BOARD.

What sum of money, at 6 per cent. will amount to $284.00 in 2yr. 6mo. 18dy., or what is the present worth of $284.00, due in 2yr. 6mo. 18dy.?

$1.00 in 2yr. 6mo. 18dy., will amount to $1.153; therefore, $1.00 is the present worth of $1.153, due in 2yr. 6mo. 18dy. Now, $284.00 contains $1.153, 246.313 times; and the present worth of $284.00 is therefore 246.313 times as much as that of $1.153, or $246.313. Hence, to find the present worth of any amount-divide by the amount of $1.00 for the time. If the present worth be subtracted from the principal, the remainder is called the discount.

31. What is the present worth of $4824.00 due in 3yr. 5mo. 6dy., at 6 per cent.? What is the discount? 32. What is the present worth of $5000.00 due in 2yr. 9mo., at 6 per cent.? What is the discount? 33. What is the present worth of $6320.00 due in 3yr. 4mo., at 5 per cent.? What is the discount?

34. What is the difference between the interest, and the discount of $1175.00 for 5yr. 7mo. 15dy., at 6 per cent.?

35. What is the present worth of $10000.00 due Jan. 1, 1850, at 6 per cent.?

EXAMPLE FOR THE BOARD.

What is the amount of $279.50, for 3yr. 5mo. 24dy., at 6 per cent., compound interest?

36. What is the amount of $131.25 for 2yr. 6mo., at 6 per cent. compound interest?

37. What is the amount of $249.00 for 3yr. 4mo. 12dy., at 6 per cent. compound interest?

38. What is the amount of $350.00 for 4yr., at 6 per cent, compound interest?

39. What is the amount of $575.00 for 5yr. 3mo., at 5 per cent. compound interest?

40. What is the compound interest of $625.00 for 5yr. 21dy., at 5 per cent?

CHAPTER VIII.

FRACTIONS.

FRACTIONS have been shown, in Mental Arithmetic, Sect. XVII., to result from division, and are expressed by writing the dividend for a numerator, and the divisor for a denominator.

A proper fraction, is less than 1, and therefore, its numerator is less than its denominator; as,

An improper fraction, is equal to, or greater than 1, and therefore its numerator is equal to, or greater than its denominator; as, 2, 3.

A mixed number, is a whole number combined with a fraction; as, 45.

A compound fraction, is a fraction of a fraction; as, of of.

An improper fraction may be reduced to a whole or mixed number, by dividing the numerator by the denominator, as in Mental Arithmetic, Sect. XVIII.

A mixed number may be reduced to an improper fraction, by multiplying the whole number by the denominator, and adding the numerator, as in Mental Arithmetic, Sect. XXIII.

A whole number may be written in the form of an improper fraction, by writing 1 for a denominator; as, 17, 17.

A compound fraction may be reduced to a simple fraction, by multiplying all the numerators together for a new numerator, and all the denominators for a new denominator, as in Mental Arithmetic, Sect. XX.

A fraction may be reduced to a decimal, by per. forming the division which is expressed by the fraction; that is, by annexing decimal Os to the numerator, and dividing by the denominator.

EXAMPLES FOR THE BOARD.

Reduce 519 to a whole Reduce 19 to twentyof of to a simple fraction. Re

Reduce 287 to a mixed number. number. Reduce 19 to fifteenths. sevenths. Reduce of duce to a decimal.

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1. Reduce 694 to a mixed number. 2. Reduce 4815 to a whole nubber.

3. Reduce 71 to an improper fraction.

4. Reduce 25 to elevenths.

5. Reduce of of of to a simple fraction.

6. Reduce to a decimal.

7. Reduce to a decimal, each of the following fractions., 16, 1, b. b. t. I, J, 1, 77, J.

5

8

9, 11

8. Reduce to a whole or mixed number, each of the following fractions: 1491, 233, 661, 1717, 365, 1844,

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9. Reduce to a simple fraction, each of the following compound fractions. of, of, of of 2, ofof, of 48.

10. Reduce to an improper fraction, each of the following mixed numbers. 4, 173, 411, 1019, 511.

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ADDITION OF FRACTIONS.

1. Add †, 4, 4, 4, § and §, and reduce the result to a mixed number.

2. Add 1, 2, § and, and reduce the result to a mixed number.

3. Add 1, 2, and 3.

4. Add 2, 3, 4 and 53.

5. Add 7, 1, 2, 3 and .

6. Add 47, 131 and 11.

29

48 115 110

7. Add 12, 12, 1, 12, and 4.

8. Add 14, 2, 3, and 4, by reducing each fraction to a decimal.

9. Add 3, 4, and 214, by reducing each fraction to a decimal, continuing the decimals to ten-thousandths. 10. Add 3, 3, and 62.

11. Add $1.564, $2.214, and $5.903.

12. A farmer sold some corn for $14.624, rye for $7.33, oats for $2.314, and barley for $5.663. How much did he receive for the whole?

EXAMPLE FOR THE BOARD.

Add 41, 33, and 24.

We cannot add sixths, fifths and sevenths, any more than tons, pounds and ounces, because they are of different denominations. We may, however, reduce them to decimals, and add, or we may reduce them to a common denominator, and add their numerators. Multiplying all the denominators together, we obtain 210. Now, if we suppose any thing divided into 210 parts, we can find the value of 6ths, 5ths, and 7ths, in 210ths. As are

210

210

equal to 1,is; is, and

are;

is, and are The above numbers are therefore equivalent to 4,350

120

210

310, and 2120, which, when added, give 10.

13. Add 6, 7, and 83. 14. Add 9, 104, and 114. 15. What is the sum of 5 16. What is the sum of 3

and 62 ?

and 4,3? 17. What is the sum of 143 and 26,4?

18. What is the sum of 4, 5, and 10?

19. What is the sum of 18%, 11, 57, and 261? 20. What is the sum of 4, 3, 5, and 14,4?

SUBTRACTION OF FRACTIONS.

EXAMPLE FOR THE BOARD.

From 142 subtract 28.

1418 1481

956

35

63

18

18

are equivalent to 13, and & to 5. We can. not subtract from ; we therefore add 1 or 63 to the of the minuend, and carry 1 to the 113 2 units of the subtrahend.

1. Subtract 11 from 213; 75 from 188; 231 from 244.

2. Subtract 141 from 154; 62 from 113; 2 from 31.

3. Subtract 9 from 10; 281 from 31; 13 from 10.

4. Subtract 1913 from 48; 54 from 67; 23% from 3325.

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5. Subtract 1211 from 145; 218 from 41; from 55.

6. Reduce the following fractions to decimals, and find their difference. 14 and 21; 30% and 4, and .

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