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7. What is the value of 4 of a hogshead of wine ?

Ans. 18gal. Oqt. Opt. 8. What is the value of 1 of a year ?

Ans. 232da. 10h. 21m. 49 41 sec. XI. To reduce any mixed quantity of weights, measures, &c. to the fractions of the integer. 1. What part of a pound is 3s. 68. ? OPERATION.,

To perform this question, 38. 6d. = 42d.

we reduce the 3s. 6d. to pence,

=to Ans. it being the lowest denomina20s.

tion in the question, and we make them the numerator of the fraction. We then reduce the one pound to pence, and make them the denom-, inator of the fraction. This fraction we reduce to its lowest terms, and we have the answer required ; wherefore the following

= 240d.

RULE.

Reduce the given number to the lowest denomination it contains for a numerator, and reduce the integers to the same denomination, for the denominator of the fraction required.

2. Reduce 4s. 8d. to the fraction of a pound.

OPERATION. 4s. 8d. = 56d. 20s.

- Ans.

= 240d.

3. What part of a ton is 4cwt. 3qr. 121b. ?

OPERATION.

5441b.

4cwt. 3qr. 121b. = 20cwt.

= 22401b.

= 17 Ans.

4. What part of 2m. 3fur. 20rd. is afur. 30rd. ?

OPERATION. 2fur. 30rd. = 110rd. 2m. 3fur. 20rd. = 780rd.

= 4$ Ans.

5. What part of 2A. 2R. 32p. is 3R. 24p. ?

OPERATION

3R. 24p. = 144p.

& Ans. 2A. 2R. 32p. = 432p. 6. What part of a hogshead of wine is 18gal. 2qt. ?

Ans. 176 17. What part of 30 days are 8 days 17h. 20m. ?

Ans. 117 8. From a piece of cloth, containing 13yd. Oqr. 2na. there were taken 5yd. 2qr. Ana. What part of the whole piece was taken ?

Ans. .

Section 21.

ADDITION OF VULGAR FRACTIONS.

I. To add fractions, that have a common denominator.

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RULE.

Write the sum of the numerators over the common de. nominator. 1. Add 7, 4, 4, 6, and together.

OPERATION

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T

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8

19

1+2+4+5+6= = 24 Ans. 2. Add t, , 11, , , and if together. Ans. 311. 3. Add ty, 14, , 17, and 17 together.

Ans. 211

Ans. 22:50 4. Add 25, 26, 2$, and Ź} together. 5. Add 17, 19, 37, and 47 together.

Ans. 24%. 6. Add 119, 137, and fun together.

Ans. 1134. 7. Add 1978, 171, and 1741 together. Ans. 11991.

II. To add fractions that have not a common denominator.

18

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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 , g, and 12 ?

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OPERATION.

126

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2) 6 8 12 2 X 3 X2 X2= 24 common denominator 3)3. 4 6

6 4 X 5=20 2)1 4 2

8 3 X3= 9 1 2 1

12 2X7=14

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24

11. Ans. 2. What is the sum of s, 11, and 18 ?

Ans. 215 3. What is the sum of 2, 1, and ? Ans. 1 27. 4. What is the sum of li, and 7?

Ans. 1477. 5. What is the sum of 1, 5, $, and I ?

Ans. 24. 6. Add $, it, and I together.

Ans. 136. 7. Add 1, $t, and together.

Ans. 11316 8. Add 25, 8, 74, and so together.

Ans. 2368 9. Add }, , , , , , and ; together. Ans. 578% 10. Add $, 1o, 11, 13, 14, 18, and if together.

Ans. 614496 11. Add of fto & of 3.

Ans. 17. 12. Add of 7 to 14 of .

Ans. 11 13. Add of to of yo.

Ans. 10 14. Add of of to $of of you

Ans. 10. 15. Add 1 of 1 of 11 to 4 of 4.

Ans. 16. Add 38 to 411.

Ans. 814 17. Add 44 to 54.

Ans. 101. 18. Add 17 to 188.

Ans. 364. 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

289

denominators over their product; thus, if it were required to find the sum of į and }, we should add the 3 and 7 together for a numerator, and multiply them together for a denominator, and the fraction would

а

be 1

19. Add 1 to 5, 7 to $, 1 to $, } to $, } to g. 20. Add to to $, tot, što je to to, to . 21. Add to , tok, to , to I'd, to }, It to it.

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 7 take g.

7-2=5, $ Ans.

Ans. 2. From It take fr

Ans. mg. 3. From if take Tg.

Ans. 4. 4. From 37 take it

Ans. tit. 5. From 167 take 1:

Ans. 38 6. From 62 take 1425 ਲ

Ans. To 7. From zo take a

Ans. . 8. From 3 take Vo.

II. To subtract fractions whose denominators are unlike.

50

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RULE.

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Reduce the fractions to a common denominator, as in Ad. dition of fractions ; then write the difference of the numerators over the common denominator.

9. From 1 take 17.

Ans. 15.

OPERATION.

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4)16. 12 4 X 4 X 3 = 48 common denominator. 4 3

161 3 x 13 = 39
12 4 X 7=28
x

11

48 Aos. 10. From 97 take 513.

Ans. 37

OPERATION.

%

9= 19,511 = 1 8 12 4 X 2 X 3 = 24 common denominator. 3

81 3 x 79= 237 1 2 2 x 71=1 42

95

-32 Ans.

24 11. From f of 127 take of 972.

Ans. 45

OPERATION.

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12 = 7:5, 972 = 42
X 7 = 23, X 1 = = 22

125 : 230
22-42, 6)48 6

8 1
6 X 8 X1=48 common denominator.

48 1 X 231=231
6 8 x 23=184

47

48 Ans. 12. From 1 take 1

Ans. 13. From 7% take it.

Ans. t. 14. From # take Zoo

Ans. 12 15. From 1 take it.

Ans. 16. From it take 16

Ans. 14 17. From 19 take it

Ans. 04 18. From 1 take is.

Ans. 1988 19. From y take robo.

Ans. 1980

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