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. of a Ans. 2s. 4d. 1. If of a yard cost of a shilling, what will yard come to? yd. yd. s. S. If : : : s. 2s. 4d. 2. If of a yard cost of a pound, what will of Ans. 3s. 4d. of a lb. of sugar cost of a shilling, what Ans. 4d. 3qrs. 1963. 1657 a yard come to? 3. If cost of a lb.? 4. If of a yard of lawn cost 7s. 3d. what will 10 yards cost? Ans 4L. 19s. 10d. 2qrs. . 5. If1 yard cost 9s. what is the value of 164 yards? Ans. 5L. 17s. 6. What is the value of 100 yards of cloth, at 11 shillings per yard? Ans. 6L. 7. If 1 ounce of silver cost 5s. what is the value of 1611oz.? Ans. 4L. 12s. 13qrs. 8. How much will 4lb. of cheese come to, at 12} cents per lb.? Ans. 552 cents. 9. What will of a pound come to, if of a lb. cost ៖ of a shilling? Ans. 4d. 10. If one yard of cloth cost 158s. 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 58cwt. of sugar, which he bartered for tea, at 83s. per lb. tea did he receive for the sugar?, at 6 d. per lb. How much. Ans. 43 lb. INVERSE PROPORTION. 1. How much shalloon, of a yard wide, will line 4 yards of cloth, 11⁄2 yard wide? 2. What quantity of shalloon, 72 yards of cloth, 1 yards wide? Ans. 9 yards. Or thus: 2×3×24089. yard wide, will line Ans. 15 yards. 3. If 16 men finish a piece of work in 283 days, how long will 12 men require to do the same work? Ans. 373 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. 149177 pieces. 6. A merchant bartered 5 cwt. of sugar at 64d. per lb. for tea at 8s. per lb. How much tea did he receive? Ans. 43lb. 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 upperfigures continually for the numerator, and those below for the denominator of the fractional answer. EXAMPLES. 1. If yard of cloth, yard wide, cost L. what is the value of yard, 1 yards wide, of the same quali ty? tyd. Byd.? :: L.: lyd. Zyd. S 70 160 76+1=3=L.-13s. 4d. Answer. 2. If 24 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 194 days labour, how much must 20 men have for 1004 days? Ans. 305L. Os. 8d. 4. If 50L. in 5 months gain 23L. interest, in what time will 13 L. gain 1L.? Ans in 9 months. 5. If the carriage of 60cwt. 20 miles cost 14 dollars, what weight can I have carried 30 miles for 5 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, too, f, are decimal fractions, and are expressed by .5, .75, .625. 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. -Million. -Hundred thousand. -Unit. -Hundred thousandth. -Thousandth. -Hundredth. -Ten thousandth. Ten Millionth. -Hundred Millionth. -Thousand Millionth. -Tenth. Whole 50 numbers. Decimals. Note. Ciphers annexed to Decimals, neither increase nor decrease their value; thus, .5, .50, .500, being, 100, 100, are of the same value: but ciphers prefixed to decimals, decrease them in a tenfold proportion; thus .5, .05, .005; being fo, T, 1800, 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. |