OPERATION. $ Ans. 3R. 24p. = 144p. 2A. PR. 32p. = 432p. 6. What part of a hogshead of wine is 18gal. 2qt. ? Ans. 126 7. What part of 30 days are 8 days 17h. 20m. ? Ans. j. 8. From a piece of cloth, containing 13yd. Oqr. 2na. there were taken 5yd. 2qr. 2na. What part of the whole piece was taken ? Ans. 4. Section 21. ADDITION OF VULGAR FRACTIONS. I. To add fractions, that have a common denominator. RULE. Write the sum of the numerators over the common de. nominator the Add 7, 4, 4, 4, and q together. OPERATION 1+2 +4 +5 + 6 = 1 = 24 Ans. 2. Add 11. DI, IT, ii, ii, and 11 together. Ans. 311. 3. Add 4, 1, 1, it, and it together. Ans. 214 4. Add z's, 25, , and it together. Ans. 225 5. Add 17, +$ 17, and 4+ together. Ans. 234 6. Add 114, 114, and together. Ans. 114. 7. Add 1971, +41, and 1741 together. Ans. 11941 II. To add fractions that have not a common denominator. RULE. Reduce mixed numbers to improper fractions, and compound fractions to simple fractions ; then reduce all the fractions to a common denominator ; and the sum of their numerators, written over the common denominator, will be the answer required. 1. What is the sum of $, &, and 12 ? OPERATION 2) 6 8 12 2 X 3 X2 X 2= 24 common denominator 3) 3. 4 6 6 4 X 5=20 2)1 4 2 8 3 X3= 9 1 2 12 2X7=14 43 24 =114 Ans. 2. What is the sum of ý, 13, and 18 ? Ans. 211 3. What is the sum of 2, 1), and Ans. 1 20 4. What is the sum of li, and 17? Ans. 1477. 5. What is the sum of 1, 6, $, and I' ? Ans. 224 6. Add $, , 31, and } together. Ans. 1381. 7. Add 1%, , and together, Ans. 123it. 8. Add 25, 48, 74, and so together. Ans. 2366 9. Add t, f, 1, 4, 5, 6, and together. Ans. 57% 10. Add g, 10, 11, 12, 14, it, and it together. Ans. 634496 11. Add f of i to of z. Ans. 145 12. Add of į to 14 of 4. Ans. 136. 13. Add f of to šof lo. Ans. Po 14. Add of off to šof of io Ans. 15. Add f of it of 11 to f of . Ans. 36 16. Add 3 to 411. Ans. 814 17. Add 44 to 5%. Ans. 1015 18. Add 171 to 18. Ans. 36. Note 1. If the quantities are mixed numbers, the better way is to add the fractional parts separately, and then to add their sum to the amount of the whole numbers. NOTE 2. If there be but two fractions to add, and their numera. tors are a unit, their sum may be found by writing the sum of the denominators over their product; thus, if it were required to find the sum of and }, we should add the 3 and 7 together for a numerator, and multiply them together for a denominator, and the fraction would be 1 19. Add to , 7 to }, to }, } tot, } to g. 20. Add to it, to $, to , t to th, to ty, to + 21. Add to , to, to , fto I's, to t, I to I. Section 22, SUBTRACTION OF VULGAR FRACTIONS. I. To subtract fractions, that have a common denominator. RULE, Subtract the less numerator from the greater, and under the remainder write the common denominator, and reduce the fraction if necessary. OPERATION. 1. From y take . 7-2=5, $ Ans. Ans. 2. From It take it Ans. tr. 3. From 11 take 15. Ans. 44. 4. From 37 take 5. From +61 take 1 Ans. 711 6. From 12 take these Ans. to. 7. From zo take y. Ans. $. 8. From take Vo. II. To subtract fractions whose denominators are unlike. Ans. Att RULE. Reduce the fractions to a common denominator, as in Addition of fractions; then write the difference of the numerators over the common denominator. 9. From 18 take Yz. Ans. 15. OPERATION. 4)16. 12 4 X 4 X 3 = 48 common denominator. 4 3 16 3 x 13=39 11 48 Aps. 10. From 97 take 514. Ans. 33 OPERATION. 4 4) 9= 4,511 = 1. 8 3 x 79=237 95 3. Ans. 24 11. From of 12% take of 977. Ans. 45. OPERATION. 12 = 76-, 972 = 42 - , 6) 48 6 8 1 48 1 X 231=231 47 48 Ans. 12. From 7 take 1 Ans. 13. From ! take it. Ans. 1. 14. From 37 take zo. Ans. 12 • 15. From take it. Ans. } . 16. From *t take 16. Ans. Het 17. From 19 take it Ans. 04 18. From 11 take to. Ans. 1988 19. From to take roto. Ans. 1980. 73 20. From of i take 1 of 4. Ans. 21. From J of 1take i'z of 13. Ans. To 22. From 71 take 37. Ans. 317. 23. From 8 take 56. Ans. 235. 24. From 91 take 37. Ans. 58. 25. From 101 take 1015. Ans. III. To subtract a proper or mixed fraction from a whole number. 26. From 16 take 11. Ans. 144. To subtract the in this example, 1 From 16 must be borrowed from the 6 in the Take 13 minuend, and reduced to fourths, (i), and the must be taken from them; from leaves. To pay for the 1, which was borrowed, 1 must be added to the 1 in the subtrahend, 1+1=2; and 2 taken from 16 leaves 14, and the f, placed at the right hand of it, gives the answer 144. The same result will be obtained, if we adopt the following OPERATION, 141 RULE. 28. 1011 Subtract the numerator from the denominator of the fraction, and under the remainder write the denominator, and carry one to the subtrahend to be subtracted from the minuend. OPERATION. 31. From 16 19 13 14 17 Take 33 911 84 611 147 154 311 54 If it be required to subtract one mixed number from another mixed number, the following method may be adopted. 32. From 94 take 3}. Ans. 534. In this question, we Minuend 94 = 945 multiply the 2 and the 7, Subtrahend 3 = 3}} the numerator and de nominator of the fraction 534 Ans. in the minuend by 5, the OPERATION |