6 a 2. What is the value of fib. Troy? Ans. 9oz. 12pwt. 3. What is the value of jó of a cwt. ? Ans. Iqr. 6şlb. 4. What is the value of of an acre? Ans. 2R. 20P, 5. What is the value of of a £ ? Ans. 6. What is the value of of a hogshead ? Ans. 52gal. 2qt. 7. What is the value of $ of a hogshead? Ans. gal. qt. 8. What is the value of of a guinea ? Ans. 4s. 8d. 2 9. What is the value of } of a lb. Troy ? Ans. pwt. 10. What is the value of of a tun of wine ? Ans. 3hhd. 3lgal. 2qt. a CASE IV. 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. 55 55 1. Reduce 4s. 7d. to the fraction of a £. We first reduce OPERATION. the given number to 4s. 7d.=55d. the lowest denomi. Then, 55 of 1 of b = £. l nation named in it, Ans. £ viz., pence. Then as the reduction is to be made to pounds, a higher de. nomination, we reduce by Case I. 2. What part of a pint is 2pk. 3qt. ? We first reduce to quarts, this being the lowest denomination 2pk. 3qt.=1991. named in it. We then reduce to the denomination of pints by 19 of 1=38 pints. Case II. OPERATION. 142. How do you reduce a compound denominate number to a fraction of a given denomination ? a 3. Reduce 2 feet 2 inches to the fraction of a yard. Ans. ifyd. 4. Reduce 3 gallons 2 quarts to the fraction of a nogshead. Ans. ishhd. 5. Reduce lqr. 71b. to the fraction of a dram. Ans. 6. What part of a hogshead is 3qt. 1 pt. ? Ans. ' 7. What part of a mile is 6ft. 7in. ? Ans. 6373960 8. What part of a mile is 1 inch ? Ans. 63560 9. What part of a month of 30 days, is 1 hour 1 minute 1 second ? Ans. 10. What part of 1 day is 3hr. 3m. ? 11. What part is 3hr. 3m. of two days ? Of 3? Of 4? Of 10? Of 25 ? a а Ans. 183 EXAMPLES IN REDUCTION. a 1. Reduce y of a pound to the fraction of a cwt. Ans. på scut. 2. If you study Arithmetic zła part of an hour, what part is it of a week? Ans. 1763 3. Bought of a pint of filberts : what part of a hogshead ? 4. What part of a mile is 5] furlongs ? Ans. 5. Bought { lb. of cloves: what part of a ton ? Ans. ato а Ans. a 6. If a fly steps į of a barleycorn, what part is it of a league ? Ans. 140480 7. If a stone covers of a square inch of land, what part of an acre does it occupy ? Ans. 3363570 8. Bought } of 3 pounds of raisins: what part of a cwt. ? Ans. 9. What part of a barrel is of 51 of 64 of a pint ? Ans. 326 10. What part of a year is į of į of 2 of 3} of an hour? Ans. 313576 . រា” a 25 2 R 11. What is of 2 of 400 bushels of wheat ? Ans. 1466% bushels. 12. Reduce y of a cwt. of sugar to the lower denomi. nations. Ans. 3qr. 21b. 12oz. 10 dr. 13. I bought of a hhd. of wine: how many gallons did I buy ? Ans. 45. 14. Reduce 7 of a pound of laudanum to the lower denominations. Ans. 23 3gr. 15. What is the value of is of an acre ? Ans. 16. A goldsmith received of a pound of gold: what is the value ? Ans. 13oz. 14 prt. 6 gr. 17. What is the value of is of a chaldron of coal ? 18. What is the value of 16 of a yard ? Ans. 2ft. din. 1}bar. 19. A man travelled of a mile: how many furlongs? Ans. 20. Reduce is of a day to the lower denominations. Ans. 12hr. 55m. 23 sec. 21. What is the value in grains of 7800 pounds Troy? Ans. 5}gr. 22. What part of an inch is a ty of an Ell English ? 23. What part of a quart is 36 of a tun? Ans. 1qt. 24. What is the value in gills of } of 14 of 2 of a hhd. ? Ans. 2016gi. 25. What part of a ton is 13cwt. 3qr. 2016. ? Ans. 27. T. 26. What part of 4cwt. Iqr. 24/b. is 3cwt. 3qr. 1776. ? 27. What part of a pound Troy is 10oz. 13pwt. Agr. ? а 400 Ans. 68 28. What part of a cord is 19fl. 11961 in. ? ? 29. What part of a mile is 13fur. 21rd. 18ft. 10in. lifbar. ? Ans. 1476 mi. 30. What part of a year is 147da. 15hr. ? . 31. What part of a hogshead is 27gal. 3qt. Ipt. ? Ans. 235 a Ans. 1181 2922 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 į of a shilling make neither £l nor 1 shilling. Neither can we add parts of the same unit unless they lare 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 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. a a a 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 addod? 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-eighthis ? EXAMPLES. =sum. 1. Add t, i, j, and together. It is evident, since all the parts OPERATION. are halves, that the true sum will 1+3+6+3=13 be expressed by the number of Hence, and halves divided by 2: that is, by thirteen two's. 2. Add of a £, of a £, and of a £ together. Ans. * of a £=£21. 3. What is the sum of ;+ + +18 + ? Ans. = 4. What is the sum of intititetit Ans. 2. a a 8 CASE II. 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. 30 1. Add , , and together. By reducing to a com OPERATION. mon denominator, the 6X3 X5=90 Ist numerator. new fractions are 4x2x5=40 2d numerator. 38+16+1=48, 2x3x2=12 3d numerator. which, by reducing to 2 X3 X5=30 the denominator. the lowest terms becomes 415. 2. Add 4 of a £, of a £, and of a £ together. Ans. £f*=£1378=£12,50 3. Add together , 1, 4, and 6. Ans. 10313 4. Find the least common denominator (see Art. 137), and add the fractions to, j, s, and g. Ans. 145. How do you add fractious which have different denominators ? How do you reduce fractions of different denominators to equivalent fractions having a commou denominator ? 3 |