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54. 249 yds. at 9s. 5d. Answer, £117. 4s. 9d. 55. 1406 yds. at 10s. 8 d. Answer, £752. 15s. 11d. 56. 558 yds. at 12s. 1d. Answer, £338. 178. 4}d. 57. 237 yds. at 14s. 10d. Answer, £175. 15s. 6d. 58. 973 yds. at 16s. 3 d. Answer, £792. 11s. 9 d. 59. 455 yds. at 18s. 5d. Answer, £418. 19s. 70. 60. 179 yds. at 19s. 11 d. Answer, £178. 16s. 3 d. 5th. When the price is pounds, shillings, pence, and farthings.

Example.
735 Cwt. at £3. 16s. 91d. per Cwt.
3

Cwt £ Multiply by the number of pounds, 2205 = 735 at 3 and take parts for the shillings, pence, 10s. .. } 367.10

and farthings, as before. 6s. 8d.. } 245 . 0 3. 1.3

Observe, 10s. the è, and 6s. 8d. id.. 1. 10.73

the of a £, are taken out of the top d.. 0. 15.34

line, which is the value of 735 Cwt.

at £l. per Cwt. It is a common £2822 . 17. 21

mistake to take these out of (2205) the wrong line.

per cwt.

1d.. d'o

Example proved.
1 Cwt. : 735 Cwt. : : £3 , 16 . 9 d.
Or, £3 . 16 .9=3687 farthings

735

18435 11061 25809

4) 2709945 farthings.

12) 677486 . 1

2,0) 5645,7. 2

£2822.17.2

Exercises.
61. 473 Cwt. at £1. 12s. 8d. Answer, £772. lls. 4d.

63. 237 Cwt. at £4. 14s. 3 d. 64. 520 Cwt. at £7. 18s. 12d. 65. 319 Cwt. at £5. lls. 10d. 66. 195 Cwt. at £13. 16s. 10 d.

Answer, £1117. 12s. O d.
Answer, £4111. 5s. Od.
Answer, £1783. 14s. 10d.
Answer, £2699. 14s. 8d.

6th. When the quantity has a fraction annexed.

Example. lbs.

d. 4371

14. 92

S.

at

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67. 3721 gal. at 5s. 9d. Answer, £107. Os. 5 d. 68. 407} gal. at 18s. 8 d. Answer, £381. 12s. 1 d. 69. 253) gal. at £3. 10s. 1 d. Answer, £889. 14s. 2 d. 70. 9761 gal, at £1. 7s. 5d. Answer, £1338. 12s. 4 d. 71. 8143 gal. at

13s. 2 d.

Answer, £538. 18s. 5 d. 72. 7034 gal. at £4. ls. 8 d. Answer, £2880. 10s. 1{d. 7th. When the quantity is of several denominations. Example. 23 Cwt. 3 qrs. 17 lb. of Sugar, £5. 18s. 5 d. per Cwt.

£ s. d.
5.18. 51 X 23

7

[blocks in formation]

10s....1
5s..
3s. 4d.
1d. 1 to
id. .

Another way.

£ s.

d. 23 Cwt. 3 qrs. 17 lb. of Sugar, at 5.18. 51 per Cwt. 5

2 grs... 2.19. 2 115

1 qr. ..}

1. 9. 71 11.10

14 lb.... 1 14. 91 5.15

2 lb....

2. 11 3.16. 8

1 lb.

1. 03
1.11
111

£5. 6. 91
5. 6. 91

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73. 177 Cwt. of Sugar, at 9 d. per lb. Answer, £79. 12s. 6d. 74. 2071 yards, at 4s. 71d. per yard. Answer, £47. 18s. 6įd. 75. 176 Cwt. 2 qrs. 10 lb. at £4. 55.71d. per Cwt.

Answer, £756. Os. 5 d. 76. 16 Cwt. 3 qr. 17 lb. at £317. 12s. 6d. per Ton.

Answer, £268. 8s. 5d. 77. 17 hdds. 14 gal. of Wine, at 3s. 45d. per pint.

Answer, £1464. 15s. 78. 175 oz. 15 dwts. of Silver, at 5s. 73d. per oz.

Answer, £49. 8s. 7d. 79. 19 Cwt. 1 qr. 18 lb. at £42. 17s. 3 d. per Ton.

Answer, £41. 12s. 80. 26 Cwt. 1 qr. 121b. at 3s. 2d. per lb.

Answer, £467.8s. 81. 729 oz. 11 dwts, of Silver, at 4s. 8d. per ounce. 82. 3 qrs. 12 lb. at £2. 6s. 10d. per Cwt. 83. 79 acres, 3 roods, 29 poles, at £8. 15s. 6d. per acre. 84. 15 Cwt. 1 qr. 19 lb. at £52. 13s. 8d. per ton. 85. 31 Cwt. 3 qrs. 7 lb. at 2s. 10d. per lb.

FRACTIONS,

ARE EITHER

VULGAR OR DECIMAL.

OF VULGAR FRACTIONS. A Fraction is a quantity which represents a part or parts of an integer or whole.

A Vulgar Fraction is represented by two numbers placed one above the other, with a line between them, as ž, ž, ý, &c. The number above the line is called the Numerator, and that below, the Denominator.

The Denominator shews into how many parts an unit is divided ; and the Numerator how many of those parts are represented by the fraction : thus, means, that an unit, as one shilling, one gallon, &c., is divided into nine parts, and five of those parts are to be taken.

Of Vulgar Fractions there are six sorts. (1.) A simple Fraction has but one Numerator, and one

Denominator, as }, {}, }, &c. . (2.) A COMPOUND Fraction is the fraction of a fraction, and

is known by the word of placed between the parts;

as į of ; ; } of ir, &c. (3.) A PROPER Fraction is when the Numerator is less than

the Denominator, as $, 5, , &c. (4.) An IMPROPER Fraction is when the Numerator is

equal to, or greater than the Denominator, as },

f, g, *, &c. (5.) A MIXED Number is composed of a whole number

and a fraction; as 4}, (6 ) A COMPLEX Fraction has a fraction or mixed number,

21
in either or both of its terms; as

7' 9
91' 37"

&c.

18%, &c.

3

8

REDUCTION OF VULGAR FRACTIONS.

CASE 1st. To find the common measure of a Vulgar Fraction.

Example.
What the common measure of 64?
252) 364 (1
252

RULE.
112) 252 (2
224

Divide the greater term by

the less, and the divisor by the 28)112 (4 112

remainder till there is no remainder. The last divisor is the

common measure.

Answer, 28 common measure.

EXERCISES. 1. What is the common measure of 13: ?

Answer, 8. 2. What is the common measure of $?

Answer, 15. 3. What is the common measure of 2

Answer, 125. 4. What is the common measure of 14?

Answer, 1728. 5. What is the common measure of 43357 ? Answer, 2223. Case 2d. To reduce a fraction to its lowest terms.

Example.
Reduce 1$to its lowest terms.
182) 196 (1
182

Rule.
14) 182(13
182

Find the common measure by
Case 1st. Then divide both nu-

merator and denominator by the 14 is the common measure :

then 14) 193=11. Answer, ii, lowest terms.

common measure.

* A Fraction still retains the same value, although reduced into lower terms. A Fraction ending with two even numbers, can be reduced into lower terms, being divisible by 2. Also, if one term of a Fraction end with 5, and the other with 0, or if both end with 5, the Fraction is divisible by 5.

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