Ans. 1 2. Add and together. Ans. 17 Ans. 2011 5. Add 1 of 95 and of 141 together. Ans. 4411 Note 1.-In adding mixed numbers that are not compounded with other fractions, you may first find the sum of the fractions, to which add the whole numbers of the given inixed numbers. for DOE 6. Find the sum of 5 7 and 15. Then ito +5+7+15=287 Ans. Ans. 17 jó Note 2.--To add fractions of inoney, weight, &c. reduce fractions of different integers to those of the same Or, if you please you may find the value of each fraction by Case VIII. in reduction, and then add them ia weir proper terms. 452 1 9. Add of a shilling to šof a pound. 1st Method. 2d Method. of=16 3.=7s.6d. Oqrs. Then oti s. 30 6 5 Whole value by Case VIII. is 8s. Od. Sqrs. Ans. Ans. 8 0 33 By Case VIII. Reduction. 10. Add lb. Troy, to of a pwt. Ans. 7oz. 4pwt. 1338r. 11. Add of a ton, to of a cwt. Ans. 12cwt. 1gr. 8lb. 12, 07: 12. Add of a mile to To of a furlong. Ins. Oftr. 28po. 13. Add of a yard, of a foot, and of a mile to Ans. 1540yds. 2ft. Iin. 14. Add 1 of a week, of a day, of an hour, and of a minute together. Anz. 2da. 2ho. Somin. 45see. ether. SUBTRACTION OF VULGAR FRACTIONS. 11 31 208 2 RULE. * PREPARE the fractions as in Addition, and the ference of the numerators written above the common nominator, will give the difference of the fraction requir EXAMPLES. 1. From take of of == Then and 1=1 tt Therefore 9-== the Ans. 2. From take Answers. 5. Froin it takes 4. From 14 take i 5. What is the difference of 1'1 and 17 ? 6. What differs its from? 7. From 144 take of 19 8. From take it O remains 9. From 1 of a pound, take of a shilling. & of y'=iipf. Then irom £. take. Ins. 316. Note.--In fractions of money, weight, &c. you may, you please, find the value of the given tractions (by Car VIII. in Reduction) and then subtract them in their pr per terms. 10. From 7. take 5 shilling. Ans. 5s. 64. 2grs. 11. From of an oz. take of a pwt. Ans. 11 pwt. 3gr. 12. From of a cwt. take of a lb. Ans. Igr. 27lb. 6oz. 10., dr. 13. From 3 weeks, take of a day, and ; off of o an hour. Ans. Sw. 4da. 12o. 19min. 17 sec 5 378 10 177 17 12 *In subtracting mixed numbers, when the lower fraction i: greater than the upper one, you may, without reducing then to improper fractions, subtract the numerator of the lower fraction from the common denominator, and to that difference. add the upper numerator, carrying one to the unit's place o the lower whole number. Also, a fraction may be subtracted from a whole number by taking the numerator of the fraction from its denominator, and placing the remainder over the denominator, then taking one from the whole number. MULTIPLICATION OF VULGAR FRACTIONS. RULE. REDUCE whole and mixed numbers to the improper fractions, mixed fractions to simple ones, and those of different integers to the same; then multiply all the numerators together for a new numerator, and all the deuominators together for a new denominator. EXAMPLES. 3 1. Multiply by Answers. = 2. Multiply s by 3. Multiply 51 by 4. Multiply sof7 by 5. Slultiply is by a 6. Multiply of 8 by of 5 131 7. Multiply 71 by 91 692 8. Multiply of by of S4 9. What is the continued product of of 3, 7,5and Ans. 45 32 81 23 DIVISION OF VULGAR FRACTIONS, RULE. PREPARE the fractions as before; then, invert the divisor and proceed exactly as in multiplication :-The products will be the quotient required. EXAMPLES. Thus, 4 X 5 1. Divide by 1 =* Ans. 3 x 7 2. Divide 17 by Answers. 145 3. Divide of by 4. What is the quotient of 17 by ?? 591 5. Divide 5 by to 6. Divide } of of 1 by off 7. Divide 4 by of 4 8. Divide 71 by 127 9. Divide 52051 by of 91 RULE OF THREE DIRECT IN VULGAR FRACTIONS, RULE. PREPARE the fractions as before, then state your question agreeable to the Rules already laid down in the Rule of Three in whole numbers, and invert the first term in the proportion ; then multiply all the three terms continually together, and the product will be the answer, in the same name with the second or'middle term. EXAMPLES. 3 s. d. qrs. 1. If of a yard cost of a pound, what will is of an Ell English cost? fyd.= of 1 of }= or Ell English. El.:. EU. As : 4 :: And xx1 = £.=10 3 1 Ans. 2. If of a yard cost of a pound, what will 400 yds. come to Ans. £59 8s. 6fd. 3. If 50 bushels of wheat cost 1711. what is it per bush Ans. 7s. Od. ijfgrs. 4. If a pistareen be worth 14; pence, what are 100 pistareers worth? 5. A Merchant sold 54 pieces of cloth, each containing 241 yds. atos sd. per yard; what did the whole amount to Ans. £60 10s. Od. 3 qrs. 6. A per having of a vessel, sells of his share for 312l. ; whe the whole vessel worth? Ans. £780 7. If 1.01 echip be worth of her cargo, valued at 88001. what is the whole ship and cargo worth? Ans. £10031 14s. 11 d. Ans. 46 INVERSE PROPORTION. 59 RULE. PREPARE the fractions and state the question as beBre, then invert the third term, and inultiply all the three tegas together, the product will be the answer. EXAMPLES. come 1. How much shalloon that is yard wide, will line 51 yards of cloth which is 11 yard wide ? Yds. yds. yds. Yds. As 11:51::3 And xx=3=16, Ans. 2. If a man perform a journey in 3 days, when the day is 12 hours long; in how many days will he do it when the day is but 9 hours. Ans. 4 days. 3. If 13 men in 11 days, mow 211 acres, in how many days will 8 men do the same. Ans. 1871 days. 4. How much in length that is 73 inches broad, will make a square foot ? ins. 20 inches. 5. If 25ès. will pay for the carriage of an cwt. 145} how far may 6 cwt be carried for the same mo ins. 29 miles. 6. How many yards of baize which is 14 yards wide, will line 187 yards of camblet yd. wide ? ins. 11yds. 1gr. 1} na.) 8. miles; ney ? 10. RULE OF THREE DIRECT IN DECIMALS. RULE. REDUCE your fractions to decimals, and state your question as in whole numbers; multiply the second and third together ; divide by the first, and the quotient will be the answer, &c. EXAMPLES. Yds. 1. If of a yd. Gost iz of a pound; what will 151 yds. come to? 13,875 15,583+and =15 £. s. d. qrs. Ans. 6.83 3. If 4dyds. cost 3s. 41d. what will 305 yıls. cost? Ans. fo.1 45 4d 2006. + |