THE SINGLE RULE OF THREE, IN VULGAR FRACTIONS. RULE. Prepare the given terms, if necessary, and state them as in whole numbers; multiply the second and third terms together, and divide the product by the first. Or, Invert the dividing term, and multiply the three terms together, as in Multiplication. EXAMPLES. 1. If of a yard cost of a shilling, what will of a yard come to? Ans. 2s. 4d. 2. If of a yard cost 75 of a pound, what will yard come to? of a Ans. 3s. 4d. 3. If of a lb. of sugar cost of a shilling, what cost of a lb. ? 1657 Ans. 4d. 3qrs. 3365. 3d. what will 10}. Ans. 4L. 19s. 10d. 2qrs. . 4. If of a yard of lawn cost 7s. yards cost? 5. If 14 yard cost 9s. what is the value of 164 yards? Ans. 5L. 17s. 6. What is the value of 100 yards of cloth, at 13 Ans. 6L. shillings per yard? 7. If 1 ounce of silver cost 5s. what is the value of 1611oz.? Ans. 4L. 12s. 13qrs. 8. How much will 45lb. of cheese come to, at 123 cents per lb.? Ans. 55 cents. 9. What will of a pound come to, if of a lb. cost of a shilling? Ans. 4,92d. 10. If one yard of cloth cost 15s. what will 4 pieces, each containing 27 yards cost? Ans. 85L. 10s. 114d. 11. A person having of a sloop, sells of his share for 319L. what is the value of the whole vessel, at that rate? Ans. 598L. 2s. 6d. 12. A merchant had 5 cwt. of sugar, at 64d. per lb. which he bartered for tea, at 8s. per lb. tea did he receive for the sugar? How much Ans. 43 lb. 2. What quantity of shalloon, 7 yards of cloth, 14 yards wide? Or thus: ××9. yard wide, will line Ans. 15 yards. 3. If 16 men finish a piece of work in 28 days, how long will 12 men require to do the same work? Ans. 37 days. 4. If 3 men can do a piece of work in 44 hours, in how many hours will 10 men do the same in? Ans. 1. 5. How many pieces of cloth, at 20 dollars per piece, are equal in value to 2404 pieces, at 12 dollars per piece? Ans. 149,177 pieces.. 6. A merchant bartered 58cwt. of sugar at 64d. per lb. for tea at 8s. per lb. How much tea did he receive? Ans. 43 lb. THE DOUBLE RULE OF THREE, IN VULGAR FRACTIONS. RULE. Prepare the given terms when necessary, by reduction, then proceed as directed in whole numbers. Or, Invert the dividing terms, and multiply the upper figures continually for the numerator, and those below for the denominator of the fractional answer. EXAMPLES. 1. If a yard of cloth, yard wide, cost L. what is the value of yard, 14 yards wide, of the same quality? #yd. : gyd. : : 3L. : 2 x 3 x3 = 180=76. 76+21=338=4L.=13s. 4d. Answer. 2. If 2 yards of cloth, 13yd. wide, cost 33L. what is the value of 38 yds. 2yds. wide? Ans. 76L. 10s. 3. If 3 men receive 8L. for 19 days labour, how much must 20 men have for 100 days? Ans. 305L. Os. 8d. 4. If 50L. in 5 months gain 237L. interest, in what time will 13 L. gain 1,,L.? Ans. in 9 months. 5. If the carriage of 60cwt. 20 miles, cost 14 dollars, what weight can I have carried 30 miles for 57 dollars? Ans. 15cwt. DECIMAL FRACTIONS. A decimal fraction is a fraction whose denominator is 1, with as many ciphers annexed as there are places in the numerator, and is usually expressed by writing the numerator only, with a point prefixed to it: thus fo, 100, 100, are decimal fractions, and are expressed by .5, .75, .625. 75 625 A mixed number, consisting of a whole number and a decimal, as 25, is written thus, 25.5. As in numeration of whole numbers the values of the figures increase in a tenfold proportion, from the right hand to the left; so in decimals, their values decrease in the same proportion, from the left hand to the right: which is exemplified in the following TABLE. -Hundred million. -Ten million. -Hundred thousand. -Ten thousand. -Hundred thousandth. -Hundredth. -Thousandth. -Ten thousandth. -Hundred millionth. -Tenth. -Ten millionth. 1 1 1 1 1 1 Whole numbers. 50 500 Decimals. Note.-Ciphers annexed to decimals, neither increase nor decrease their value; thus .5, .50, .500, being 10, 100, 1000, are of the same value: but ciphers prefixed to decimals, decrease them in a tenfold proportion; thus, .5, .05, .005; being fo, Too, Too, are of different values. ADDITION OF DECIMALS. RULE. Place the given numbers according to their values, viz. units under units, tenths under tenths, &c. and add as in addition of whole numbers; observing to set the point in the sum exactly under those of the given numbers. 6. Add.5, .75, .125, .496, and .750 together. 7. Add.15, 126.5, 650.17, 940.113, and 722.2560 together. 8. Add 420., 372.45, .270, 965.02, and 1.1756 together. SUBTRACTION OF DECIMALS. RULE. Place the numbers as in addition, with the less under the greater, and subtract as in whole numbers; setting the point in the remainder under those in the given numbers. Multiply as in whole numbers: then observe how many decimal figures there are in both factors, and point off that many figures, for decimals, in the product. If there are not so many figures in the product as there are decimal figures in both factors, prefix ciphers to supply the deficiency. |