20 London is indebted to Genoa in 1710/ 16s 4d.; for how many pezos may Genoa draw on London, the exchange at 47d. per pezo ? answer 8644+ 21 How many millreas will 15661 6s 8d. amount to, exchange at 64d. per millrea? answer 5873 millreas, 750 reas. 22 A merchant in Rotterdam remits 564/ 10s 6d. Flemish, to be paid in London; how much sterling money must he draw for, exchange at 34s 4d. per pound sterling? answer 328/ 16s 11d. 23 Amsterdam changes on London 345 3d. per . sterling, and on Lisbon, 52d. Flemish, for 400 reas; how then ought the exchange to go between London and Lisbon ? answer 75d. sterling, nearly, per millrea. 24 A, at Paris, drrws on B, of London, for 1200 crowns, at 55d. sterling per crown; for the value whereof, B draws again on A, at 56d. sterling per crown; besides commission per cent. what did A gain or lose by this transaction? answer A gained 15+ crowns. A VULGAR FRACTIONS. VULGAR FRACTION is a part, or parts of an integer, and is noted thus,, one-eighth;, seveneighths. The upper number is called the numerator, and shews the part, or parts, expressed by the fraction; the lower number is called the denominator, and denotes the number of such parts contained in a unit. Vulgar fractions are either proper, improper, compound, or mixt. A proper fraction is one of which the numerator is less. than the denominator; thus, 7, +1. 88 An improper fraction is que which the numerator is equal to, or greater than, the denominator; thus, &, . A compound fraction is, a fraction of a fraction; as, of of, &c. A mixt number consists of a whole number and a fraction; as, 73. A mixt fraction has a fraction annexed either to its nu 428 7 merator or denominator; as, 2, or, or 73 REDUCTION REDUCTION OF VULGAR FRACTIONS. CASE 1.. To reduce a fraction to its lowest terms, RULE. Divide the greater term by the less, and that divisor by the remainder, till nothing be left: the last divisor will be the common measure; by which divide both terms, for the fraction required: or, Take the aliquot parts of both terms continually, till in their lowest terms. Note. If the common measure be 1, the fraction is already in its lowest terms. Ciphers to the right hand of both terms may be rejected, thus, 783. 2) 700 EXAMPLES. 1 Reduce 48 to its lowest terms. Or, 4) 48)56(18)+(= facit. 48=49 facit. 48 Com. measure 8)48(6· To reduce several fractions to others, retaining the same value, and to have one common denominator; RULE.. Reduce the given fractions to their lowest terms: then multiply each numerator into all the denominators but its own, for its respective numerator; and all the denominators into each other, for a common denominator. Note. This cafe, and cafes, prove each other. EXAMPLES. 3 74 facit 338, 315, 7 and 148 Reduce,,, and to a common denominator. 4 Reduce,, 5 Reduce,, 1616 183 facit 136 1379 T 1188 and 693 and, to a common denominator. 36 144 6 1386 facit 33, 34, 384 and 444 and, to a common denominator. facit 12, 120, 200 and 60 CASE 3. To reduce a mixt number to an improper fraction; RULE. 240 To the product of the whole number, with the denominator, add the numerator, for a new numerator, under which plaee the given denominator. 1 Reduce 12 2 Reduce 19 3 Reduce 16, 4 Reduce 100 5 Reduce 514 1 EXAMPLES. to an improper fraction. 12×17+15=29 facit. to an improper fraction. 6 Reduce 47 to an improper fraction. CASE 4. 354 ठ 16.18 5919 39 8229 T6 39794K 8400 To reduce an improper fraction to a whole or mixt num RULE Divide the upper term by the lower. Note. This case, and case 3, prove each other. 1 Reduce 1 to its proper terms. 17)219(12 17 facit. To reduce a compound fraction to a single one; RULE. Multiply all the numerators together for a new numerator, and all the denominators for a new denominator. Note. Like figures in the numerators and denominators may be cancelled, and frequently others contracted, by taking their aliquot parts. CASE 6. To reduce the fraction of one denomination to the fraction of another, but greater, retaining the same value; RULE. Make it a compound fraction, by comparing it with all the denominations between it and that to which it is to be reduced; which fraction reduce to a single one. EXAMPLES. 1 Reduce & of a penny to the fraction of a pound. 40L. facit. 2 Reduce of a farthing to the fraction of a shilling. facits. 3 Reduce of an oz. troy to the fraction of a lb. facit lb. 4 Reduce of a lb. avoirdupois to the fraction of a C.wt. facit C.ut. 5 Reduce of a pint of wine to the fraction of a hhd. facit hhd. 6 Reduce 40 of a minute to the fraction of a day. CASE 7. facit day. To reduce the fraction of one denomination to the fraction of another, but less, retaining the same value; RULE Multiply the given numeror by the parts of the denomination between it and that to which it is to be reduced, for a new numerator, and place it over the given denominator; which reduce to its lowest terms. Note. This case, and case 6, prove each other. EXAMPLES. of a L. to the fraction of a penny. 5X20X12-1228=d. facit. 144 of a shilling to the fraction of a farthing. 1 Reduce 2 Reduce facit qr. 3 Reduce of a lb. troy to the fraction of an oz. facit foz. L |