15. What is the interest of $999.00 for 10mo. 27dy., at 6 per cent.? What is the amount? 16. What is the interest of $25.00 for 11mo. 18dy., at 6 per cent.? What is the amount? 17. What is the amount of $375.00 for 9yr. 6mo., at 6 per cent.? 18. What is the amount of $625.00 for Syr. 9mo., at 7 per cent.? 19. What is the amount of $1456.00 for 19dy., at 6 per cent.? 20. What is the amount of $799.00 for 24dy., at 9 per cent? EXAMPLE FOR THE BOARD. Find the interest of $4632.25, for 3yr. 7mo. 21dy., at 6 per When the rate is .06 for lyr. or 12 months, it will be .03 for 6 months, .12 for 24 months; and generally, half as many hundredths as there are months. Then, for 1mo. or 30dy., the rate would be of .01 or .005; for as of a month, or 6 days, it would be .001, and generally many thousandths as are equivalent to the number of days. Hence the following rule to find the rate for any given time at .06 per annum. Call the years and months reduced to months, so many hundredths, and call the days so many thousandths. Divide the hundredths by 2, and the thousandths by 6, and the sum of the two quotients will be the rate required. 21. What is the interest of $2984.00 for 2yr. 8mo. 27dy., at 6 per cent.? 22. What is the interest of $1449.00 for 3yr. Imo. 21dy., at 6 per cent.? 23. What is the interest of $9999.00 for 5yr. 11mo. 3dy., at 6 per cent.? 24. What is the interest of $5000.00 for 7yr. 10mo. 6dy., at 6 per cent.? 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 percent.? 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, 1⁄2, A mixed number, is a whole number combined with a fraction; as, 40. 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, Y. 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. 287 EXAMPLES FOR THE BOARD. Reduce 2 to a mixed number. number. Reduce 1975 to fifteenths. sevenths. Reduce of of of Ts duce to a decimal. 513 Reduce 5s to a whole Reduce 19 to twentyto a simple fraction. Re 1. Reduce 34 to a mixed number. 2. Reduce 415 to a whole nubber. 3. Reduce 714 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.,,,,,,,,,, 8. Reduce to a whole or mixed number, each of the following fractions: 1491,203,681,177, 305, 1844, 2230 11 9. Reduce to a simple fraction, each of the following compound fractions. of, of, of of 2, ៖ of of, of 48. 10. Reduce to an improper fraction, each of the following mixed numbers. 417, 41%, 10%, 5. ADDITION OF FRACTIONS. 1. Add 육, 육, 즉, 수, 육 and 육, and reduce the result to a mixed number. 2. Add,, and, and reduce the result to a mixed number. 8. Add 14, 2, 4, and, by reducing each fraction to a decimal. 9. Add , 훅, and 214, by reducing each fraction to a decimal, continuing the decimals to ten-thousandths. 10. Add 3,, and 62. 11. Add $1.564, $2.214, and $5.904. 12. A farmer sold some corn for $14.62, rye for $7.334, oats for $2.314, and barley for $5.664. How much did he receive for the whole? EXAMPLE FOR THE BOARD. Add 4, 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 210 are |