23. Add s. to 3d. fs.+3d.=24d.+3d.=73d.+1fd.=§gd.=577,d., Ans.; or, fs.d.3s.+1s. = 38s.+s. 1s., 2d Ans. = 1st Ans. 24. Add gal. to qt. 25. Add together bush. pk. and §qt. 26. Add together ton cwt. and qr. Ans. qt. or gal. (c) To add two fractions that have a common numer ator: Multiply the sum of the denominators by either numerator, and place the product over the product of the denominators. 27. What is the sum of 2 and 3? 1 1 8+7 15 3 3 + + 8 ; .. 7 X 8 56 14=17, Ans. Add the sum of the fractions to the sum of the integers. 30. What is the sum of 3 and 43? #+3=38+18=43=1,7%; 3+4=7; 31. What is the sum of 54, 3%, and 12%? 36. What is the sum of 38, 63, and 37. What is the sum of 3, 42, 83, and 25? 38. How many are 83+3 +83+14? 152. Mode of adding two fractions that have like numerators? Mode of adding mixed numbers? PROBLEM 15. 153. To subtract a less fraction from a greater: RULE. Prepare the fractions as in addition, and then write the difference of the numerators over the common denominator. (a) — }=118, Ans. (See Art. 152, a). Ans. X-X=3—4=}}-38, Ans. 22. From of take of fr 23. From 4 of 1 take 3 of 1%. 24. From of 10 take of 2. 25. From 14 of 7 take § of 1. 26. From off of } take off of §. Ans. 3. 153. Rule for subtracting one fraction from another? How are the fractions prepared in addition? 30. From s. take d. (See Art. 152, b). (b) s.-fd.d.-fd.—§fd.-zd.§3d.=138d., Ans. or, s. d. 48. s. = 62008.-08.5s., 2d Ans. = 31. From qt. take pt. 32. From ton take cwt. 33. From acre take rod. Ans. qt. or 1дpt. Ans. 188a. or 6733rd. NOTE. The answer to these examples may be in any denomination of the table. 34. From of a week take of an hour. (c) To subtract when the fractions have a common numerator: Multiply the difference of the denominators by either numerator, and write the product over the product of the denominators. (d) To take a mixed number from a whole or mixed number. 38. From 6 take 23. 62341, Ans. (See Art. 152, d). 153. Mode of subtracting when the fractions have a common numerator? 39. From 8 take 271. 8-27-714-27=5, Ans. In Ex. 38, take from , and 2 units from 6 units; but in Ex. 39 we cannot take from,.. reduce one of the 8 units to, and add it to the, making 14, and then take the 1, and the 2 units from the remaining 7 units. 40. From 9 take 35. from 4. Add 8 to 611. 5. Subtract 1815 from 2517. 6. Reduce 23 to an improper fraction. 7. Reduce 8 to a fraction whose denominator is 27. 8. Reduce 9 to 6 fractional forms. 9. Divide by 13. 10. Divide 16 by 23. 11. Divide by 5. 12. Reduce of a day to hours, minutes, and seconds. 13. Reduce 3pk. 5qt. 1pt. to the fraction of a bushel. 14. Multiply 8% by 10. 15. Divide 93 by 4. 16. Divide by 9. 17. Divide 18 by 3. 18. Reduce 374 to a mixed number. 25 19. Reduce 1128 to a whole number. 20. Multiply 3 by 11. 21. Reduce 22. Subtract of off to a simple fraction. from 3. 153. Mode of taking a mixed number from a whole or mixed number? 23. Reducer, , and to equivalent fractions that have a common denominator. 24. Reduce 1, 2, and 37 to equivalent fractions having the least common denominator. 25. Reduce and to equivalent fractions having a common numerator. 26. Reduce, , and 18 to equivalent fractions having the least common numerator. 30. Reduce by 4. of a gallon to the fraction of a quart. 31. Reduce of an hour to the fraction of a week. of of of 1 32. Reduce 33. Multiply by 33. 34. Multiply 25 by . to its simplest form. 35. Multiply 25 by 3. 36. Divide by §. 37. Add £, s., and d. together. 38. Subtract of a gill from of a gallon. 39. Add , fo, fs, fo, and 1 together. 40. From take 33. 41. Five gallons, 3 quarts, 1 pint, and 3 gills, are what part of 1 gallon? (See Art. 152, Note 3). 42. Three pecks are what part of 3 pecks? EXAMPLES IN ANALYSIS. 154. We analyze an example when we proceed with it, step by step, according to its own conditions, without being guided by any particular rule. Ex. 1. If 4 tons of hay cost $48, what will 7 tons cost? SOLUTION. If 4 tons cost $48, then 1 ton will cost of $48, which is $12; and if 1 ton cost $12, then 7 tons will cost 7 times $12, which is $84, Ans. |