2. In 3804 crowns, how many pieces each 7s. 6d. ? 3. In 7284 florins, each 3s. 2d. how many pounds? 4. How many times will a wheel 16ft. in circumference turn round in a distance of 24 mi. 3 fur. 25 po.? 5. A grocer wishes to weigh up 8cwt. 2qrs. 20lbs. of sugar into an equal number of parcels of 4 lbs. 6 lbs. 8 lbs. 10 lbs. 12 lbs. and 14 lbs. each, what number will he have of each, and how many altogether? Weight of 1 parcel of each kind (4+6+8+ 10 + 12 +14) lbs. 54 lbs. 1. II. REDUCTION OF FRACTIONS. TO EXPRESS IN LOWER TERMS THE VALUE OF A FRACTION OF A Rule. Multiply the fraction by the number of the next lower denomination, which make up one of the higher; reduce the result to a whole or mixed number. Proceed in the same manner with the fractional part, if any, till the lowest denomination required is arrived at. If the fraction be a recurring decimal, it must be reduced to a vulgar fraction. EXAMPLES. 1. Express in lower terms the value of of a crown. ... ..10714285 = 10s. 8 d. TO EXPRESS IN HIGHER TERMS THE VALUE OF A FRACTION OF A Rule. Divide the fraction by the number of the lower denomination which make up one of the next higher, and the quotient in like manner, till the denomination required is arrived at. If the fraction be a vulgar fraction, reduce it to its lowest terms; if a decimal, leave it unaltered. TO EXPRESS A COMPOUND QUANTITY AS A FRACTION OF ANY Rule. Begin with the quantity of the lowest denomination, express this as a fraction of the next higher. Add to the result the quantity of this denomination, and express the sum as a fraction of the next higher. Proceed in the same manner through all the quantities, and if the result be not in the required denomination, express it by Case II. But if the required denomination be arrived at before all the quantities have been used, those not used must be reduced to the denomination required. EXAMPLES. 1. Express 17 p. 4 yds. 2 ft. as a fraction of a league. IV. TO EXPRESS SHILLINGS, PENCE, AND FARTHINGS AS DECIMALS OF A POUND. Rule. Put in the 1st place of decimals 1 for every pair of shillings:in the 2nd and 3rd places, 50 for the odd shilling, if any, and 1 for every farthing besides, with 1 extra for sixpence :-in the 4th and 5th places, put 4 for every farthing above the last sixpence, and 1 extra for every 6 farthings:-to fill up the places after the 5th, form a fraction, whose numerator is the number of farthings above the last 6, and whose denominator is 6; convert this into a decimal, and annex the figures of the decimal to the others. EXAMPLE. Change 17s. 7 d. to the decimal of a pound. 17s. 7.8822916 £. Ꮴ . TO EXPRESS IN POSITIVE TERMS THE VALUE OF A DECIMAL OF A POUND. Rule. Take 2 shillings for every 1 in the 1st place; 1 shilling for 50 in the 2nd & 3rd, and 1 farthing for every 1000th remaining, after subtracting 1, if the number exceed 24. Note. This rule gives generally only approximately the value of the decimal:-if the fraction of a farthing be required, multiply the given decimal by 1000, and subtract from the product 4 per cent.-this will give the exact number of farthings: whence the true result may be easily obtained. Find the value of .754321 £. EXAMPLE. .754321 £= 15s. 1d. Approx. by Rule. But 1000 X .754321 = 754321 And 40 X.754321 = 30.17284 VI. TO EXPRESS IN POSITIVE TERMS THE VALUE OF A FRACTION OF A COMPOUND QUANTITY. Rule. Express the compound quantity in terms of any one of the denominations involved; multiply the two fractions, and reduce the results. |