14. What is the value of 5 of 15 yards of cloth? 15. What is the value of of a tun of wine? 16. What is the value of 17. What is the value of 18. What is the value of 19. What is the value of 20. What is the value of 3 of a butt of beer? II 7 of a year? of a chaldron of coal? of 15cwt. 3qr. 14lb.? 21. What is the value of 3 of a cubic yard? 22. What quantity of ale is contained in § of 15228 cubic inches, English measure? CASE IV. 124. To reduce a denominate number to a denominate fraction of a given denomination. Reduce the 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 £. OPERATION. 4s. 7d. - 55d. We first reduce the given number to the lowest denomination Then, 55 of named in it, viz., pence. of 1 = £55. 12 20 Then, as the reduction is to be made to pounds, a higher de nomination, we reduce by Case I. 2. What part of a bushel is 2pk. 3qt.? We first reduce to quarts, this being the lowest denomination. We then reduce to bushels by Case I. OPERATION. 2pk. 3qt. 19qt. 19 of of =2bu 1 1 QUEST.—124. How do you reduce a denominate number to a fraction of a given denomination? 3 Reduce 2 feet 2 inches to the fraction of a yard. Ans. 4. Reduce 3 gallons 2 quarts to the fraction of a hogshead. 5. Reduce 1qr. 7lb. to the fraction of a hundred. Ans. 6. What part of a hogshead is 3qt. 1pt.? Ans. 7. What part of a mile is 6ft. 7in.? Ans. 8. What part of a mile is 1 inch? Ans. 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.? Ans. Ans. 11. What part is 3hr. 3m. of 2 days? Of 3? Of 4? Of 10? Of 25 ? 12. Reduce 15s. 11d. to the fraction of a pound. 13. Reduce 51d. to the fraction of a shilling. 14. Reduce lcwt. 2qr. 6lb. 3oz. 88dr. to the fraction of a cwt. 15. Reduce 5oz. 31gr. to the fraction of a lb. troy. 16. Reduce 3qr. 31na. to the fraction of an English ell. 17. Reduce 147da. 15hr. to the fraction of a year. 18. What part of a pound is 15s. 91d.? 19. What part of a groat is of three halfpence? 20. Reduce 4bu. 22pk. of corn to the fraction of a quarter. 21. Reduce 1gr. 3na. to the fraction of a yard. 22. Reduce 2R. 15P. to the fraction of an acre. 23. Reduce 20 11gr. to the fraction of a H. 24. Reduce 3qt. 1pt. 2gi. to the fraction of a hogshead. 25. Reduce 184 cubic inches to the fraction of a cubic yard. 26. Reduce 17bu. 3pk. to the fraction of a London chaldron. 27. Reduce 24′ 33′′ to the fraction of a degree. 28. Reduce 27gal. 3qt. 1pt. to the fraction of a hogshead, beer measure ADDITION OF VULGAR FRACTIONS. Addition of integer numbers is the process of finding a single number which shall express all the units of the numbers added (ART. 48.) Addition of fractions is the process of finding a single fraction which shall express the value of all the fractions added. It is plain that we cannot add fractions so long as they have different units: for, of a £ and 1⁄2 of a shilling make neither £1 nor 1 shilling. Neither can we add parts of the same unit unless they are like parts; for of a £ and 1 of a £ make neither nor of a £. But of a £ and 2 they make of a £. of a £ of a £ may be added: and of a £ make 3 of a £. So, of a £ Hence, before fractions can be added, two things are necessary. 1st. That the fractions be reduced to the same denomination; that is, to the same unit: 2d. That they be reduced to to a common denominator; that is, to the same fractional unit (ART. 94). CASE I. 126. 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. QUEST.-125. What is addition of integer numbers? What is addition of fractions? 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 one-fourth without reduction? 126. 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 fourfourths? Of three-fifths, six-fifths, and two-fifths? Of three-sixths, sevensixths, and nine-sixths? Of one-eighth, three-eighths, and four-eighths? 3 4. What is the sum of++Å++? 3 15 6. What is the sum of ++ f + li + 1} + }} ? CASE II. 10 11 13 11 127. When the fractions are of the same denomination but have different denominators. Reduce complex and compound fractions to simple ones, mixea numbers to improper fractions, and all the fractions to a common denominator. Then add them as in Case I. 2. Add of a £, of a £, and of a £ together. 3. Add together 1, 1, 4, and 6}. Ans. 4. Find the least common denominator (Art. 119) and add the fractions, 2, 3, and 4. Ans. QUEST.-127. How do you add fractions which have different denominators? How do you reduce fractions of different denominators to equiva lent fractions having a common denominator? 5. Find the least common denominator and add 6 3 4 12, Ans. 6. Find the least common denominator and add ¦ of }, of 19, and of 12 together. 9 Ans. 7. Add 3, of of, and of of 11 together. 10 II 128. When there are mixed numbers, instead of reducing them to improper fractions we may add the whole numbers and the fractional parts separately and then add their sums. 2. Add together 31, 65, 85, and 65%. Ans. 6. Add together 62, 133, 183, and 1322. Ans. 7. Add 3, 4, and together. 9 11 8. Add and of of 153 together. 10 II Ans. Ans. 129. When the fractions are of different denominations. Reduce the fractions to the same denomination. Then reduce all the fractions to a common denominator, and then add them as in Case I. QUEST.-128. How may you proceed when there are mixed numbers? 129. When the fractions are of different denominations, how are they added? What is the second method? |