not agree in their estimates, they determined to take their average judgment, and let that be the value; what was the value in that case ? A $ 100 80 4 )470 $117,50c. Ans. 2. Four persons appraising a building, A valued it at • $550,50c., B, at $480,50c. C, at $590,50c. and D, at $600; what was the mean value ? Ans. $555,371c. 3. Seth Strong, Luke Locke, Mark Mills, Charles Church, and John Jones, were appointed to appraise the ship Ocean; Strong's estimate was $5500, Locke's $7000, Mill's $6666, Church's $8444, and Jones's, $5000; what was the mean judgment ? Ans. $6522. DUODECIMALS. DUODECIMALS chiefly regard feet and inches. They are so called, because they decrease by twelve from the place of feet towards the right hand. Inches are sometimes called primes, and marked thus ('); the next division is called parts or seconds, and marked ("); the next thirds, and marked (""); &c. MULTIPLICATION OF DUODECIMALS. . Rule.—Under the multiplicand write the corresponding denomination of the multiplier. Multiply each term in the multiplicand, beginning at the lowest, by the highest denomination in the multiplier ; and write each result under its respective term; observing to carry a unit for every 12 from each lower place to its next higher. In the same manner multiply all the multiplicand by the next highest denomination in the multiplier; and set G the result of each term removed one place to the right hand of those in the multiplicand. Proceed in like manner with the remaining denominations, and the sum of all the lines will be the product required. EXAMPLES. 1. Multiply 4 feet 2 inches by 3 feet 5 inches. Ft. I The 2 in the product 4 2 is not 2 inches, but 2 3 5 twelfths of a square foot, or 24 inches, &c. 12 6 1 8 10" 14 2 10 Ans. 2ft. 2' 10". 2. Multiply 10 feet 11 inches by 7 inches. 10 11 7 6 4 5 Ans. 6ft. 4' 5". 3. What is the content of a bale 6 feet 5' long; 4 feet 3' high, and 3 feet 10' wide ? Ft. 1 25 8 27 3 3 81 9 9 NY 104 6 5 6 Ans. 104ft. 6' 5" 6". 4. What is the content of a marble slab 4ft. 7' 8" wide and 5ft. 6' long? Ans. 25ft. 6' 2". 5. Multiply 7ft. 8 6" by 10ft. 4' 5". Ans. 79ft. 11' 0" 6" 6". 6. Multiply 44ft. 21 9" 21" 4''"' by 2ft. 10' 3". Ans. 126ft. 2' 10" 8" 10" 11". 7. How many square feet in a board 25 feet 6 inches long, and I foot 3 inches wide ? Ans. 31 feet 104 inches. 8. How many cubic feet in a stick of timber 12 feet 10' long, 1 foot 7' wide, and I foot 9'thick ? Ans. 35ft. 6' 8" 6"". 9. How many cubic feet of wood in a load 7 feet 16' long, 3 feet 11' wide and 3 feet 6' high ? Ans. 107ft. 4' 7". 10. The length of a room being 20ft., its width 14ft. 6', and height 10ft. 4'; how many yards of painting are in it, deducting a fire-place of 4ft. by 4ft. 4!, and two windows, each 6ft. by 3ft. 2'? Ans. 732 yards. 11. Required the solid contents of a wall 53ft. 6' long, 10ft. 3' high, and 2ft. thick. Ans. 1096ft. 9'. FRACTIONS. FRACTIONS, or broken numbers, are expressions for any assignable parts of a unit, or whole number, and, generally, are of two kinds, viz. VULGAR AND DECIMAL. A Vulgar Fraction is represented by two numbers, placed one above the other, with a little line drawn between them; thus, , , &c. signify three-fourths, fiveeighths, &c. The figure above the line, is called the numerator, and the one below the line the denominator. 5 Numerator. Thus 8 Denominator. The denominator (which is the divisor, in division,) shows how many parts the unit or integer is divided into; and the numerator (which is the remainder after division,) shows how many of those parts are meant by the fraction: A fraction is said to be in its least or lowest terms, when it is expressed by the least numbers possible ; thus A when reduced to its lowest terms, will be 1, and is when expressed by the least numbers possible, will be *; and so of any others. PROBLEM 1. To abbreviate or reduce fractions to their lowest terms. RULE.—Divide the terms of the given fraction by any number which will divide them without leaving a remainder, and the quotients divide again in like manner; and so on till it appears that there is no number greater than 1, which will any longer divide them; and then the fraction will be in its lowest terms. 15 16 324 EXAMPLES 1. Reduce 427 to its lowest terms. 8433=84 638= 3) = the answer. 2. Reduce 193 to its lowest terms. 3. Reduce to its lowest terms. 4. Reduce 45 to its lowest terms. 5. Abbreviate non as much as possible. 6. Bring $26 to the least terms possible. 7. Reduce 114 to its lowest terms. 8. Abridge as low as you can. 9. Put 171 into its least terms. 10. Let 684 be expressed in its least terms. Ans. 1 Ans. 1 Ans. Ans. 14 Ans. Ans. Ans. š. Ans. 18 Ans. 32 180 6 9 12 PROBLEM 2. To find the value of a fraction in the known parts of the integer, as of coin, weight, measure, foc. RULE.—Multiply the numerator by the common parts of the integer, and divide by the denominator, and the several quotients set in one line, will show the answer. EXAMPLES. 1. What is the value of 4 of a pound sterling? Numer. 2 20 shillings in a pound. Denom. 3)40( 13s. 4d. the Ans. 3 10 9 1 3)12(4d. 12 2. What is the value of 13 of a pound sterling? Ans. 18s. 5d. 21rs. 3. Reduce of a shilling to its proper quantity. Ans. 4d. 3jqrs. 4. What is the value of g of 12s. 6d. ? Ans. 4s. 84d. 5. What is the value of i of a pound Troy? Ans. Joz. 6. How much are 11 of a hundred weight ? Ans. 3qrs. 7tt. 10,402. 7. What is the value of f of a mile ? Ans. 6fur. 26pol. 11ft. 8. How much are of a cwt., at 25th to a qr. ? Ans. 3qrs. 21. 12oz. 7fdr. 9. Show the proper quantity of of an ell English ? Aus. 2qrs. 3fna. 10. How much are & of a hhd. of wine ? Ans. 54 gallons. 11. What is the value of 9 of a day? Ans. 16h. 36m. 552 s. 12. What is the value of $ of a dollar ? Ans. 80cts. PROBLEM 3. To reduce any given quantity to the fraction of any greater denomination of the same kind. Rule.-Reduce the given quantity to the lowest term mentioned, (as in reduction of Money, Weights, Meas |