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2. Add and together.
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 mixed numbers.
6. Find the sum of 53 74 and 15.
I find the sum of 3 and 4 to be 21-111
of of 5
NOTE 2.-To add fractions of money, weight, &c. reduce fractions of different integers to those of the same.
Or, if you please you may find the value of each frac tion by Case VIII. in reduction, and then add them in their proper terms.
9. Add 4 of a shilling to of a pound.
4 of 10-1406. Then+120£• Whole value by Case VIII. is 8s. Od. Sqrs. Ans.
11. Add of a ton, to
12. Add 3 of a mile to
10. Add lb. Troy, to & of a pwt.
13. Add of a yard, gether.
14. Add 4 of a week, a minute together.
2d Method. 3.7s. 6d. Oqrs. $s. 0 6 3
Ans. 8 0 3
Ans. 7oz. 4pwt. 134gr.
Ans. 12cwt. 1gr. 8lb. 12, oz:
Ins. Ofur. 28po.
SUBTRACTION OF VULGAR FRACTIONS.
PREPARE the fractions as in Addition, and the difference of the numerators written above the common denominator, will give the difference of the fraction required.
Then and 71 π
2. From 25 take
5. What is the difference of and 17?
6. What differs
13.2 T5 5 378 10 177 1_7 12
7. From 144 take of 19
8. From 3 take
9. From of a pound, take of a shilling N77 off. Then from 11. take. Ans. 31. NOTE. In fractions of money, weight, &c. you may, if you please, find the value of the given fractions (by Case VIII. in Reduction) and then subtract them in their pro
of a lb.
10. From take 37 shilling. Ans. 5s. 6d. 24qrs. 11. From of an oz. take of a pwt.
Ans. 11pwt. 3gr.
12. From of a cwt. take
Ans. 1qr. 27lb. 6oz. 108, dr. 13. From 3 weeks, take of a day, and of of of an hour. Ans. Sw. 4da. 12ho. 19min. 174sec
*In subtracting mixed numbers, when the lower fraction is greater than the upper one, you may, without reducing them 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 of 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 denominators together for a new denominator.
1. Multiply by
9. What is the continued product of of 3, 7, 5 and of ?
DIVISION OF VULGAR FRACTIONS.
| Answers. 12=}
8. Divide 71 by 127
9. Divide 5205 by of 91
PREPARE the fractions as before; then, invert the divisor and proceed exactly as in multiplication :-The products will be the quotient required.
4 x 5
3 X 7
1. Divide by
2. Divide 17 by
4. What is the quotient of 17 by ?
5. Divide 5 by
6. Divide of of by of
7. Divide 45 by § of 4
RULE OF THREE DIRECT IN VULGAR
PREPARE the fractions as before, then state y question agreeable to the Rules already laid down in Rule of Three in whole numbers, and invert the first t in the proportion; then multiply all the three terms c tinually together, and the product will be the answer the same name with the second or middle term.
1. If of a yard cost of a pound, what will of Ell English cost?
yd. Ell. £. Ell. As ::
of of 8 or Ell English.
come to ?
And 4xx.10 3 15 A 2. If of a yard cost of a pound, what will 40 y 18 Ans. £59 8s. 61d. If 50 bushels of wheat cost 1737. what is it per bus Ans. 7s. Od. 13grs4. If a pistareen be worth 143 pence, what are 100 p tareens worth P Ans. £
5. A merchant sold 54 pieces of cloth, each containin 244 yds. at 95% sd. per yard; what did the whole amou Ans. £60 10s. Od. 3grs. 6. A person having of a vessel, sells of his share f 3121.; what the whole vessel worth? Ans. £780 7. If of a ship de worth 2 of her cargo, valued 8000l. what is the whole ship and cargo worth? Jins. £10031 14s. 11d.
PREPARE the fractions and state the question as be fore, then invert the third term, and multiply all the thre teams together, the product will be the answer.
1. How much shalloon that is yard wide, will line 5 yards of cloth which is 14 yard wide? Yds. yds. yds.
As 13:53 And 4x11x4-335-16, 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. 444 days. acres, in how many Ans. 1833 days. inches broad, will Ans. 20 inches.
3. If 13 men in 113days, mow 21 days will 8 men do the same. 4. How much in length that is 7 make a square foot ?
5. If 254s. will pay for the carriage of an cwt. 1451⁄2 miles; how far may 6 cwt. be carried for the same moAns. 22 miles. ney? which is 14 yards wide, yd. wide?
6. How many yards of baize will line 183 yards of camblet
Ans. 11yds. 1gr. 1 na.
RULE OF THREE DIRECT IN DECIMALS.
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.
1. If of a yd. cost of a pound; what will 153 yds.
come to ?
Yds. £. £. s. d. grs.