Reduce 45 $ to £ sterling. What is the value of 6 lb 4 oz 45x+8=10,125, or 45 40troy of standard filver, or filver 10,125 A. 20 $2,500 12 (T. 2.) 11 parts fine? ་ d 6,000 (pro. inverted or 6 lb 4 oz-76 oz. x 321 40 T.1.) 89,026 A. nearly bufhels of grain will 45 $=10,125£=10£. 2s. 6d. =6£ 75s 90d. How many a Reduce 100 lbs. troy to lbs. hold? avor. 700 100 x 7682,2857 A. 700 371 (T 9. pro. between ft & bu.398 5 x 5 x 4 100 ft x 9 80,323 bu. A. What is the avordupois weight of 20 pipes of water, (allowing A. in. 8298,00 the cafks to weigh 14 tuns ?) 1 Subtract the lower number from the upper; but where the lower number is the largest, subtract it from [the common divisor or] A.1 so many as make one of the next denomination and add the remainder to the upper number, set down this sum for the remainder required, add one to the next lower number and subtract as before. lb. A. 1013. A 24 10 10-rs 22 x 48(382)10A. SIMPLE DIVISION, MULTIPLICATION and ADDITION. Divide each number by the divisor,set down the quotient and multiply the remainder by a number that will reduce it to the next lower denomination, add this sum to the given number of the same denomination and divide as before. Tuns. C. T. C. 4)15 15 (3 183 A. -r3x20=60 cwt. THE RULE OF THREE, IN GEOMETRICAL PROPORTION, Is a compofition of multiplication and divifion, which takes its name from the number of terms given; it is also called the rule of proportion,* because the ratio or proportion, existing be ween the given quantity or cause and its required price or effect, is given in numbers of the fame quality. RULE. When the answer is to be larger than the given number of the fame name or quality, multiply this number by the larger of the two other given numbers, that are alike in quality; but, when the answer ought to be leis, multiply the number, that is of the ame name of the answer, by the least of the two other given numbers, divide the product by the other and the quotient is the number required For proof invert the question,makingthe answer a part. (See Dem. of Rules.) EXAMPLES. If 2 yds. of cloth coft 3 & what will 8 yards coft? Here 3 S is of the fame name or quality of the answer, which must be larger than 3 therefore xy by the largest of the fimilar numbers, viz 8 yds. and divide the product by the other, viz. 2)24(128 A. If 8 yds coft 12 $ what will 2 yds cost? Here the answer is to be less than the given number of the fame name, viz. 12 therefore xy by the leaft of the fimilar numbers, viz. 2 yds &e by the other i.e. the largest of the two, viz. 8)24(3 A. [and proof of the first.] To flate or arrange numbers Proportionally. RULE. Place the quantity or caufe for the firft term, whofe price or effect is given, (which place) for the fecond term, and *Place any quantity or cause under a line, and its price or effect above, and this fraction is the true proportion between any other quantity or cause of the same kind and its price or effect, and is the exact price or ef fect of 1. If any number be xd by the proportion which it bears to that which is required, the product is the answer. the quantity or caufe for the third, whose price, effect or anfwer is required for the fourth term, which may be found as before by multiplying the 2nd & 3rd terms together and dividing their product by the 1ft or fuch a number* as will bring the 1ft term to the 2d will bring the 3d to the 4th. So the 1ft and 3d terms are alike in quality, and the 2d and 4th will also be fimilar. As any caufe is to its effect, fo is any greater or lefs caufe, of the fame kind, to its effect. Or as an effect is to its cause, so is another effect fimilar, to its cause. If 40$ are equal to 9£ fterling, how many are 2700 $ worth? As 408 9: 2700 $: 607,5 £. or 2700x=607,5 £ : 9 40)24300(607,5£. A. Here 40 % is the quantity whofe price (9) is given. And 2700 $ is the quantity whofe price is required. 40% and 2700 $ are alike in quality, and so ae 9£ & 607,5£. $ As 607,5 2700 :: 9:40 $ proof. If either the 2d or 3d term be divided by the divifor and the quotient multiplied by the other the product is the answer. If 3 lbs be worth 12 cts, what is 36 lbs of the fame,worth? As 3 lbs: 12 cts: 36 lbs: 144 cts. or 36 x 12-144cts. 3)12(4 x 36 144 cts 3)36(12 x 12-144 A. Here 4 will increase 3 to 12, therefore it will increase 36 to 144 the A. As 3x4: 12 :: 36x4: 144. If 4 Maffachusetts, are equal to 3 fterling, how many fterling are equal to 100£ Maff.? This NUMBER is the RATIO existing between the 1st & 2nd terms of the statement, also between the 3rd & 4th, and may always be found by g the 2nd term by the 1st. When there are two terms given, one an atecedent or cause, the other its consequent or effect, they show the relation between any other antecedent or cause of the same kind, and its consequent or effect; so the RATIO, between a cause of one kind and its effect, is similar to that between all other causes of the same quality and their effects, and VICE VERSA. As 4 Mafs: 3 Sterl: 100 Mafs: 75 Sterl A. or 100 x 2=75° A. If a staff 3 ft long cast a fhade 2 ft; how high is that steeple or tree whofe fhadow, at the fame time, is 75 ft, the ground being level? As 2, fhade: 3, height: 75, fhade: 112,5 ft height. A. A bushel is to a cubic foot as 371 is to 298 (Table 9.) bsh. As 298 bsh: 371 ft :: 120 bsh: 149,4 .-ft A. 120 ft 298)44520(149,4 cubic ft contents. or 120 x 27=149 4 - ft If 20 gallons of water weigh 167 lbs; what will 10 hhds. of 63 glns each, weigh? (Table 11 Wine Meas.) As 20 glns: 167 lbs :: 10x 63 glns: 52604 lbs A. 630 20)105210(5260 If 100 $ gain 6 in 1 year; what will 400 $ gain in 2 years? As 100 x 1 : 6 :: 400 x 2 : 48 § A. When any of the given numbers are vulgar fractions; reduce them to decimals and proceed as before, or reduce the two numbers of the fame name to those having a common divifor and use their dividends as integers, or invert the 1ft term and multiply the three terms together and the product will be the answer, or 4th term. If 2 lb cost 4 dimes, what is 2 4 lb worth? As ,75 lb 4 di. :: 2,5 lb : 13,333di A. 4)3,00,75 lb, 2=2,5, lb 4 ,75)10,0(13,333 or 4, 24=1; x =10 As 3: 4 di : 10: 13 di. A or †, inverted §, 24—§‚ 4d=†,‡ סס=';=13} di A. 21 |