5. Find the least common denominator and add i, j, , and 30 Ans. 1 146. When there are mixed numbers, instead of re. ducing them to improper fractions we may add the whole numbers and the fractional parts separately, and then add their sums. 1. Add 197, 63, and 4 together. Whole numbers. Fractional parts. 19+6+4=29. }+s+=183=1180 Hence, 29+1,046=30045, the sum. 5 2. Add 31, 6, 815, and 65%. Ans. 8448 OPERATION. 64 64 7 280 CASE III. 147. When the fractions are of different denomina. tions. Reduce the fractions to the same denomination. Then reduce all the fractions to a common denominator, after which add them as in Case I. EXAMPLES. a 25 5 a a 3 1. Add şof a £ to ã of a shilling. of a £=of 20= 40 of a shilling. Then, 40 +==116+=28.=858.=14s. 2d. Or, the ã of a shilling might have been reduced to the fraction of a £ thus, of =lio of a £= of a £. Then, ģ+24=42+*=of a £: which being reduced, gives 14s. 2d. Ans. 14s. 2d. 2. Add of a yard to ý of an inch. Ans. Blyd. or 14 şin. 3. Add of a week, of a day, and of an hour together. Ans. da. hr. 4. Add 1 of a cwt., 851b., and 3 %02. together. Ans. 2qr. 2316. 13,0%. 146. How do you add when there are mixed numbers ? 147. How do you add fractions of different denominations? a 5. Add 14 miles, y furlongs, and 30 rods together. Ans. Im. 3fur. 13rd. 148. The value of each of the fractions may be found separately, and their several values then added. EXAMPLES. 1. Add of a year, of a week, and of a day together. of a year = of 365 days=219 days. 3 hours. Ans. 221da. 11hr. 2. Add of a yard, of a foot, and of a mile together. Ans. yd. ft. in. 3. Add of a cut., 2 of a lb., 130%., and } of a cwt. 616. together. Ans. lcwt. 2qr. 17lb. 13oz. EXAMPLES IN ADDITION. 1. I bought 22, bushels of wheat at one time, 19'z at ancther, and 33, at another: how much did I buy in all ? Ans. 7528 bu. 2. What is the sum of 26, 187, 193, 137, and 17 ? 3. A farmer owns three farms; the first contains 47112 acres, the second 714jó, and the third 1814: how many acres in all ? Ans. 136837 acres. 4. Bought 1 of 32 of 5cwt. of sugar at one time; at another, of 51 of 6cwt. ; at another, } of of 8cwt. : how much did I buy in all ? Ans. 2013. cut. 5. What is the value of of a ton, and of a cut. ? Ans. 12cwt. 1qr. 716. 130%. 6. How far is of a mile and to of a furlong? 7. A man travelled 287 miles the first day, 334 the second day, and 2921 miles the third day: how far did he travel in all ? Ans. 90mi. 4fur. 15rd. 3ft. 114in. 42 а a 148. How may fractions of different denominations be added by the second method ? of an hour, and for 8. Add 5 days and 52 minutes together, and give the whole time. Ans. 5da. 20hr. 52m. 151 sec. 9. What is the entire weight of cut. 8 lb. and 37%oz.? Ans. 2qr. 1616. 3oz. 835dr. io. Find the value of } of a year, } of a day, of} 24 Ans. 21 11. Bought 3 pieces of cloth; the first contained of 3 3 of of yards; the second off of 5; and the third of of i: what did they all contain ? Ans. 2yd. 2gr. llna. 12. Add together , , 13, and 1815. Ans. 31105 13. Add together 16, 4, 1, and . Ans. 4791 14. Add together 384, 13], and 9. Ans. 15. Add together 64, 134, 1715, and 132. Ans. 1691 16. Add together of a week, of a day, and one hour. Ans. 17. Add together 1_cwt. 173lb. and 70%. Ans. lcwt. 1gr. 716.78 02. 4 237 3 SUBTRACTION OF VULGAR FRACTIONS. 149. It has been shown that before fractions can be added together, they must be reduced to the same unit and to a common denominator. The same reductions must be made before subtraction. SUBTRACTION of Vulgar Fractions is the process of find. ing the difference between two fractions. CASE I. 150. When the fractions are of the same denomination and have a common denominator. 149. Can one-third of a shilling be subtracted from one-third of a £ without reduction? Can one-sixth of a shilling be subtracted from one-fifth of a shilling? What reductions are necessary before subtraction? What is subtraction ? 150. How do you subtract fractions which have a common unit and the same denominator ? Subtract the less numerator from the greater and place the difference over the common denominator. EXAMPLES. 1. What is the difference between s and j? Ans. 3. From take 168 Ans. 4. From 497$ take 1697. Ans. 5. From 18906 take 2009 Ans. 17997 38 365 166 105 9765• 327 327 327 CASE II, 151. When the fractions are of the same denomination, but have different denominators. Reduce mixed numbers to improper fractions, compound and complex fractions to simple ones, and all the fractions to a common denominator : then subtract them as in Case I. EXAMPLES. 1. What is the difference between and f? Here, -=-== answer. 2. What is the difference between 12 of and 2 ? Ans. is 3. What is the difference between 21 of a £, and is of a £? Ans. 4. From of 6, take 19 of 1. 5. From of of 7, take of Ans. 6. From 371}, take 3 of }. Ans. 3635 Ans. 18 CASE III. 152. When the fractions are of different denomina. tions. 151. How do you subtract fractions which have the same unit but different denominators? What is the difference between one-half and one-third ? 152. How do you subtract fractions which are of different denominations? Reduce the fractions to the same denomination : then reduce them to a common denominator, after which subtract as in Case I. EXAMPLES. a a a 60 1. What is the difference between 1 of a £ and l of a shilling? } of a shilling=} of zo=66 of a £. Then, 1-2=30-2=2% of a £=9s. 8d. 2. What is the difference between į of a day and of a second ? Ans. 11hr. 59m. 59 sec. 3. What is the difference between of a rod and of an inch ? Ans. 10ft. 11 in. 4. From 1 of a lb., Troy weight, take of an ounce. 5. What is the difference between is of a hogshead, and is of a quart? Ans. 16gal. 2qt. Ipt. 3 sgi. 6. From of a £ take of a shilling. Ans. 7. From oz. take pwt. Ans. 11pwt. 3gr. 8. From 4 cut. take 4 lb. Ans. 4cut. 3qr. 61b. 1oz. dr. a GENERAL EXAMPLES. a 1. From šof an ounce take į of a put. Ans. 6pwt. 15gr. 2. Take of a day and i of of of an hour from 3 weeks. Ans. 3. A man engaged to work 41 days, but was absent by indisposition 646 days: how many days did he work? Ans. 34 16 days. 4. What remains of a hogshead of vinegar if of it has leaked out? Ans. 5. A man has travelled 4mi. 1fur. 24rd. : how much farther must he go in order to make6 miles ? Ans. 2mi. 2fur. 16rd. 6. From 1 take 1oo Ans. 7. From 9 take 1. Ans. 7} 8. From of a degree take of a mile. Ans. 67 a |