5. Find the value of 10714285 of £5. 10714285 - 10 X 100 s. 11. TO EXPRESS IN HIGHER TERMS THE VALUE OF A FRACTION OF A SIMPLE QUANTITY. 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. EXAMPLES. 1. Express 4-yd. as a fraction of a mile. 3 3 mi. =- mi. 4 x 1760 7040 2. Express pole as a fraction of a league. 3 3 mi. 1 -lea. =- lea. 7 X 40 X 8 X 3 2240 3 Express .345895 of 1s. as the decimal of £1. .345895 s. 20 .01729475 £. Ans. -po. = 4. Express 6.461538 of Id. as decimal of £1. 6.461538 d. 12 .538461 s. 20 ,02692307 £. Ans. III. TO EXPRESS A COMPOUND QUANTITY AS A FRACTION OF ANY SIMPLE QUANTITY. 6 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. 1 5 2— ft. = - yd. 6 po. = - po. 6 2 33 29 590 590 17– po. = lea. 33 33 33 X 40 X 8 X3 59 lea. lea. Ans. 3168 2. Express £1:13: 6 as the decimal of £1. 4)3.0000 f. 12)6.7500 d. 2,0)13.5625 s. 1.678125 £. Ans. -- po. = 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. 74d. to the decimal of a pound. 17s. 71 =.8822916 £. V. TO EXPRESS IN POSITIVE TERMS THE VALUE OF A DECIMAL OF A POUXD. Rule. Take 2 shillings for every 1 in the 1st place; 1 shilling for 50 in the 2nd & 3rd, and 1 farthing for every 10ooth 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. EXAMPLE. Find the value of .754321 £. .754321 € = 15s. 1d. Approx. by Rule. .:: No. of farthings = 724.14816 .754321 £ = 15s. ld. .14816 fa. 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. EXAMPLES. 1. Exprese in positive terms 2 of £1: 2: 2. 3 11 1 4 6 of £1 £=3--- £. 480 480 £. =- S. -S d.= 11. d. 2 .. 28 of £1: 2:2= £3:0:114. 2. Express in positive terms 1.7658 of £1: 13: 41. £1:13:44 = 1.66875 €. 1.66875 1335000 834375 1001250 1168125 166875 2.946678750 £. 20 18.93357500 s. 12 11.202900 d. 4 2.8116 fa. Ans. £2: 18:11 .8116 fa. VII. TO EXPRESS ONE QUANTITY, FRACTIONAL OR OTHER, IN TERMS, OR AS A FRACTION, OF ANOTHER. Or, TO FIND THE RATIO of one TO THE OTHER. Rule. Express both quantities in the same denomination, and divide the former by the latter. Leave the result, as a vulgar, or decimal fraction, as required. EXAMPLES. 1. Express 2s. 74d. as a fraction of 3s. 4d. 5 8 1 3 28 3} 10 X 8 63 80 2. Express 4 of 3ac. as a fraction of 2 r. 202 po. 1 1 7 7 8 2 41 41 2 80 1 1 7 1 of 3- ac. = of 2r. 204 2 238 2 280 201 79 =1 201 3. Express 3s. 73das the decimal of 9s. 6d. 5 8 1 2 3.625 9.5 1. TO ADD SEVERAL COMPOUND QUANTITIES OF THE SAME KIND TOGETHER. Rule.-1. Write the quantities under each other, placing those of the same denomination in the same column. 2. Add the column of the lowest denomination ; convert the sum into a number of the next higher denomination. 3. Carry this number to the next column, and set down the remainder under the first. 4. Add the next column, in the same way, and repeat the operations till the last column is added. EXAMPLES. 1. Add together the following quantities £4: 10:1}; £25: 13: 5%; £67 : 10 : 0}; £0: 3:01. £. $. d. 4 10 13 25 13 5 67 10 0. 0 3 02 |