5. What is the value of 1⁄2 of a £? 6. What is the value of of a hogshead? Ans. Ans. 52gal. 2qt. 7. What is the value of 186 of a hogshead? 504 8. What is the value of of a guinea? Ans. 4s. 8d. 9. What is the value of 3 of a lb. Troy? Ans. oz. pwt. 10. What is the value of of a tun of wine? CASE IV. Ans. 3hhd. 31gal. 2qt. 142. To reduce a compound denominate number to a fraction of a given denomination. Reduce the given number to the lowest denomination mentioned in it: then if the reduction is to be made to a denomination still less, reduce as in Case II.; but if to a higher denomination reduce as in Case I. EXAMPLES. 1. Reduce 4s. 7d. to the fraction of a £. We first reduce the given number to the lowest denomination named in it, viz., pence. Then as the reduction is to be made to pounds, a higher denomination, we reduce by Case I. 2. What part of a pint is 2pk. 3qt.? We first reduce to quarts, this being the lowest denomination named in it. We then reduce to the denomination of pints by Case II. OPERATION. 2pk. 3qt. 19qt. 19 of 38 pints. 142. How do you reduce a compound denominate number to a fraction of a given denomination? 3. Reduce 2 feet 2 inches to the fraction of a yard. Ans. yd. 4. Reduce 3 gallons 2 quarts to the fraction of a hogsAns. hhd. head. 5. Reduce 1qr. 77b. to the fraction of a dram. 6. What part of a hogshead is 3qt. 1pt.? 7. What part of a mile is 6ft. 7in. ? 8. What part of a mile is 1 inch? Ans. Ans. Ans. 360 79 63360' Ans. 83360. 9. What part of a month of 30 days, is 1 hour 1 minute 1 second? 10. What part of 1 day is 3hr. 3m.? 11. What part is 3hr. 3m. of two days? Of 10? Of 25 ? Ans. Ans. 183 Of 3? Of 4? EXAMPLES IN REDUCTION. 1. Reduce of a pound to the fraction of a cut. Ans. cut. 2. If you study Arithmetic part of an hour, what part is it of a week? Ans. 37837 3. Bought of a pint of filberts: what part of a hogshead? 4. What part of a mile is 5 furlongs? Ans. 77 Ans. 5. Bought 3lb. of cloves: what part of a ton? 3 Ans. gooo 6. If a fly steps of a barleycorn, what part is it of a league? Ans. 1140480 7. If a stone covers of a square inch of land, what part of an acre does it Ans. 363520* 8. Bought cwt.? occupy ? of 3 pounds of raisins: what part of a Ans. 9. What part of a barrel is of 5 of 61 of a pint? 10. What part of a year is of of 21 of 33 of an hour? 25 Ans. 313376° 11. What is of 24 of 400 bushels of wheat? Ans. 4663 bushels. 12. Reduce of a cut. of sugar to the lower denominations. Ans. 3qr. 2lb. 12oz. 10 dr. 13. I bought of a hhd. of wine: how many gallons did I buy? Ans. 45. 14. Reduce 107 of a pound of laudanum to the lower denominations. Ans. 23 3gr. 15. What is the value of 16. A goldsmith received is the value ? 17. What is the value of 18. What is the value of ៖ of an acre? Ans. of a pound of gold: what Ans. 13oz. 14pwt. 6gr. of a chaldron of coal? of a yard? Ans. 2ft. 8in. 1}bar. 19. A man travelled of a mile: how many furlongs? Ans. 20. Reduce of a day to the lower denominations. Ans. 12hr. 55m. 23sec. 21. What is the value in grains of 800 pounds Troy? 22. What part of an inch is 23. What part of a quart is Ans. 5gr. of an Ell English? of a tun? Ans. 13qt. 24. What is the value in gills of 3 of 11 of 23 of a hhd. ? Ans. 2016gi. 25. What part of a ton is 13cwt. 3qr. 207b.? Ans. 279T. 400 26. What part of 4cwt. 1qr. 247b. is 3cwt. 3qr. 17/b.? 27. What part of a pound Troy is 10oz. 13pwt. 8gr.? Ans.. 28. What part of a cord is 19ft. 1196in.? 29. What part of a mile is 13fur. 21rd. 18ft. 10in. 1}}bar. ? Ans. 14765mi. 30. What part of a year is 147da. 15hr.? 6864 1181 Ans. 2922 Ans. 233. 31. What part of a hogshead is 27gal. 3qt. 1pt.? ADDITION OF VULGAR FRACTIONS. 143. Addition of integer numbers teaches how to express all the units of several numbers by a single number. Addition of fractions teaches how to express the value of several fractions by a single fraction. It is plain, that we cannot add fractions so long as they have different units: for, of a £ and of a shilling make neither £1 nor 1 shilling. Neither can we add parts of the same unit unless they Vare like parts; for of a £ and of a £ make neither of a £ nor of a £. But of a £ and of a £ may be added: they make of a £. So, of a £ and 2 of a £ make of a £. Hence, before fractions can be added, two things are necessary. 1st. That the fractions be reduced to the same denomination. 2d. That they be reduced to a common denominator. CASE I. 144. When the fractions to be added are of the same denomination and have a common denominator. Add the numerators together, and place their sum over the common denominator: then reduce the fraction to its lowest terms, or to its equivalent mixed number. 143. What does addition of integer numbers teach? What does addition of fractions teach? What two things are necessary before fractions can be added? Can one-half of a £ be added to one-half of a shilling without reduction? Can one-half be added to onefourth without reduction ? 144. When the fractions are of the same denomination and have a common denominator, how do you find their sum? What is the sum of one-third and two-thirds? Of three-fourths, one-fourth, and four-fourths? Of three-fifths, six-fifths, and two-fifths? Of threesixths, seven-sixths, and nine-sixths? Of one-eighth, three-eighths, and four-eighths? 2. Add of a £, & of a £, and of a £ together. Ans. 15 of a £=£2}. 3. What is the sum of 3+++13+16? 4. What is the sum of CASE II. Ans. 42=1. 145. When the fractions are of the same denomination but have different denominators. Reduce compound and complex fractions to simple ones, mixed numbers to improper fractions, and all the fractions to a common denominator. Then add them as in Case I. EXAMPLES. 1. Add 1⁄2, 1, and together. By reducing to a common denominator, the new fractions are 38+18+13=3, which, by reducing to the lowest terms becomes 41. OPERATION. 6×3×5=90 1st numerator. 2. Add of a £, & of a £, and & of a £ together. 75 378 248 Ans. ££1,7% = £125. = 378 3. Add together 4, 1, 4, and 6}. Ans. 10318. 4. Find the least common denominator (see ART. 137), and add the fractions,,, and . Ans. 145. How do you add fractions which have different denominators? How do you reduce fractions of different denominators to equivalent fractions having a common denominator? |