CASE II. from a whole number, Ruli.Subtract the numerator of the fraction from its denominator, and put the denominator of the fraction under the remainder ; and carry one to be deducted from the whole number. Examples. 12 — }=113 Ans. 2. It is required to subtract 27from 32. Ans. 4 49 97 3. What is the difference between 12 and 21 ? Ans. 87 1 8 10. 4. What is the difference between 101 and 100 Ans. 7 000 99 ? 100 CASE III. To subtract fractions having different denominators. RULE..Reduce the fractions to a commop de nominator, by case 5th, in Redaction; and the difference of the numerators is the difference required. Examples. 19 20 45 22 83 are equal to dif. Ans. 45 180 180 180 171 88 19 and 2. What is the difference between and 15 Ans, 5 10 . 30 CASE IV. To distinguish the largest of any two fractions, &C.. Rule.-Reduce them to a common denominator, (by case 5th in Reduction,) and the one that has the largest numerator is the largest fraction.. Example. reduced to a common denom. is equal to 54 10 1 Ans. 60 Therefore is the largest fraction. CASE V. To subtract a mixed number from a mixed number, be taken from. 12 Examples 129. less by 89 19 72 114 57 I14 ୨9 Anson 114 3 114 To subtract when the fractions are of different de. nominations, such as parts of cwt. qr. lb. &c. RULE.Find the value of the fraction (by case 10th in Reduction, then subtract as in compound subtraction. If fractions happen in finding the value of the parts, reduce them to common denominators and subtract as in case third. Examples. 1. It is required to take of a cwt. from of a ton. 2. Required to take ing of a cwt. from 12 cwt. Ans. 12 cwt. O qrs. 18 lb. 10 oz. 103 dr. MULTIPLICATION OF VULGAR FRACTIONS. CASE I. RULE.Reduce compound fractions to simple multiply the numerators all together for a new nuones ; mixed numbers to improper fractions; then merator, and the denominators for a new denomi nator. Examples. 2 %. It is required to multiply 24, by 1 of gi Ans. 66 64 164 5 9 3. It is required to multiply iz by io Ans. of IVISION OF VULGAR FRACTIONS, Rule.-Reduce compound fractions to simple ones; mixed numbers to improper fractions ; theninvert the divisor(that is put the numerator for the denominator) and multiply the numerators together for a new numerator, and the denominators together for a new denominator ; and the fraction thus found is the quotient required. Examples. inverted is x Ans. 2. It is required to divide by si 100 Ans..7 3. It is required to divide 10 by off. Ans. 3316 4. It is required to divide 10% by 7 249 Ans. 1 6 540 Miscellaneous Questions in Vulgar Fractions: 1. A schoolmaster being asked one dày how many scholars he had, made answer that one fifth of them sat on one seat, one tenth on another, two fifths on another, two tenths on another, and 6 on another ; I demand the number his school consisted of. of 2 of =.54 to 6. = 60 Ans, 2. A man, having returned from a journey, was asked by a friend, what his expenses were ; the answer was, that he spent in Boston of his money ; between Boston and New York }; in New York ; beyond New York sto; and he brought home $40; I demand the sum he. carried, and also what he spent. Ans. carried $160, and spent $120.. 1 1 2 2 10 tof-t -X-10--9 = 1=5 10 5 10 10 1 10 1 RULE OF THREE IN VULGAR.FRACTIONS:. RULE.-State the question as in the Rule of Three Direct, invert the divisor, and multiply the numerators together, and the denominators together, and the frac. tion thus found is the fourth term or answer ; com.pound fractions must be reluced to simple ones, and mixed numbers to improper fractions. Examples. 1 75 2 1 75 3 As : 2 100 1. If - bushel of corn cost of a dollar, what will 100 of a bushel come to ? Dols. 2 x x 3 inverted is Ans: 1 X 100 X 4 2. If 104 bushels of potatoes cost $34; how many may be had for $121? 44 Ans: 39 400 3. If 4 of of a ship is worth of 16000 dollars ; show much is of of her worth? Ans. $4571.42.8384 |