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NOTE.

As half a foot is equal to 6 inches, we add them to the 5 inches, which make 11 inches. The same principle is adopted in the 14th, 15th, and 16th examples.

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19£. Os.

10d. 3qr.

1. What is the sum of 16£. 5s. 8d. 2qr.—31£. 16s. 11d. 3qr.-21. 11s. 1qr. 3qr. and 28£. 17s. 5d. 1qr.?

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13£. 13s. 7d. Ans. 131£. 5s. 84d.

2. Bought of a London tailor a vest for 1£. 13s. 4d., a coat for £. 12s. 9d., pantaloons for 2£. 3s. 9d., and surtout for 9£. 8s. Od.; what was the whole amount ?

Ans. 20£. 17s. 10d.

3. Bought a silver tankard, weighing 1lb. 8oz. 17dwt. 14gr., a silver can, weighing 1lb. 2oz. 12dwt., a porringer, weighing 11oz. 19dwt. 20gr., and three dozen of spoons, weighing 1lb. 9oz. 15dwt. 10gr.; what was the whole weight?

Ans. 5lb. 9oz. 4dwt. 20gr.

4. What is the weight of a mixture of 3lb 43 23 29 14gr.. of aloe, 2lb 73 63 19 13gr. of picra, and 1b 103 13 29 17gr. of saffron ? Ans. 7b 103 33 19 4gr. 5. Add 32lb 93 13 29 14gr.; 13 b 73 63 19 13gr.; and 16tb 113 73 19 12gr. together.

Ans. 63lb 43 73 29 19gr. 6. Sold 4 loads of hay; the first weighed 27cwt. 3qr. 18lb.; second, 31cwt. 1qr. 15lb.; third, 19cwt. 1qr. 15lb.; and fourth, 38cwt. 2qr. 271b.; what is the weight of the whole ?

Ans. 117cwt. 1qr. 19lb. 7. Bought 5 pieces of broadcloth; the first contained 17yd. 3qr. 2na.; second, 13yd. 2qr. Ina. ; the third, 87yd. 1qr. 3na.; the fourth, 27yd. 1qr. 2na.; and the fifth, 29yd. 1qr. 2na. what was the whole quantity purchased?

Ans. 175yd. 2qr. 2na.

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8. A pedestrian travelled, the first week, 371m. 3fur. 37rd. 5yd. 2ft. 10in.; the second week, 289m. 2fur. 18rd. 3yd. 1ft. 9in.; and the third week he travelled 399m. 7fur. 3ft. 11in.; how many miles will he have travelled?

Ans. 1060m. 5fur. 16rd. 5yd. 1ft. 9. A man has 3 farms; the first contains 186A. 3R. 14p. ;

the second, 286A. 17p.; and the third, 115A. 2R.; how much do they all contain? Ans. 588A. 1R. 31p. 10. The Moon is 5s. 18° 14' 17" east of the Sun; Jupiter is 7s. 10° 29′ 28′′ east of the Moon; Mars is 11s. 120 11' 56" east of Jupiter; and Herschel is 7s. 180 38′ 15′′ east of Mars; how far is Herschel east from the Sun ?

Ans. 7s. 29° 33′ 56′′.

11. I have 4 piles of wood; the first contains 7 cords, 76ft. 167lin.; the second, 16c. 28ft. 56in.; the third, 29c. 127ft. 1000 in.; and the fourth, 29c. 10ft. 1216in.; how much is there in all? Ans. 82c. 115ft. 487in. 73hhd. 43gal. 3qt. 1pt. of another, 15hhd. 3qt. 1pt.;

12. A vintner sold at one time wine; at another, 27hhd. 3gal.; at

and at another, 161hhd. and 2qt.; how much did he sell in all? Ans. 276hhd. 48gal. 1qt.

13 A man has 3 sons; the first is 14y. 3mo. 2w. 5d. old; the second is 9y. 10mo. 3w. 4d. 23h. 12m. 15sec.; and the third is 2y. Imo. 3w. 2d. 7m.; what is the sum of their ages? and how much older is the first than the second ?

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Ans. 26y. 3mo. 1w. 4d. 23h. 19m. 15sec. 4y. 5mo. 3w. Od. Oh. 47m. 45sec. NOTE. When 4 weeks are reckoned as a month, it requires 13 months to make one year.

14. I have 73A. of land; if I should sell 5A. 3R. 1p. 7ft., how much should I have left ? Ans. 67A. OR. 38p. 2654ft. 15. A. owes B. 100£.; what will remain due after he has paid him 3s. 6d. ? Ans. 99£. 16s. 5±d. 16. It is about 25,000 miles round the globe; if a man shall have travelled 43m. 17rd. 9in. how much will remain to be travelled? Ans. 24,956m. 7fur. 22rd. 15ft. 9in. 17. Bought 7 cords of wood; and 2 cords 78ft. having been stolen, how much remained ? Ans. 4c. 50ft. 18. I have 15 yards of cloth; having sold 3yd. 2qr. Ina., what remains ? Ans. 11yd. 1qr. 3na. 19. If a wagon loaded with hay weighs 43cwt. 2qr. 18lb., and the wagon is afterwards found to weigh 9cwt. 3qr. 23lb., what is the weight of the hay? Ans. 33cwt. 2qr. 23lb.

20. Bought a hogshead of wine, and by an accident 8gal. 3qt. 1pt. leaked out; what remains ? Ans. 54gal. 1pt.

21. I had 10A. 3R. 10p. of land; and I have sold two houselots, one containing 1A. 2R. 13p., the other, 2A. 2R. 5p.; how much have I remaining? Ans. 6A. 2R. 32p. 22. The Moon moves 13° 10′ 35' in a solar day, and the

Sun 59′ 8′′ 20"; now supposing them both to start from the same point in the heavens, how far will the Moon have gained on the Sun in 24 hours? Ans. 12° 11' 26" 40".

23. A farmer raised 136bu. of wheat; if he sells 49bu. 2pk. 7qt. 1pt., how much has he remaining?

Ans. 86bu. 1pk. Oqt. 1pt. 24. If from a stick of round timber, containing 2T. 18ft. 1410in., there be taken 38ft. 1720in., how much will be left? Ans. 1T. 19ft. 1418in. 25. If from 1lb. of ipecacuanha there be taken at one time 43 23 13gr., and at another, 33 13 29 14gr., how much will be left? Ans. 43 33 29 13gr. 26. A brewer has in one cellar 18bbl. 3gal. 2qt. of beer, and in another, 13bbl. 1p.; what is the whole quantity, and how much more is in one cellar than the other?

Ans. 31bbl. 3gal. 2qt. 1pt. 5bbl. 3gal. 1qt. 1pt.

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27. If from $100.00 there be paid at one time $ 17.28,5, at another time $ 10.00,5, and at another $37.15, how much will remain ? Ans. $35.56.

SECTION XII.

REDUCTION.

THE object of Reduction is to change the denomination of numbers without altering their value. It consists of two parts, Descending and Ascending. The former is performed by Multiplication, the latter by Division.

Reduction Descending teaches to bring numbers of a higher denomination to a lower; as, to bring pounds into shillings, or tons into hundred weights.

Reduction Ascending teaches to bring numbers of a lower denomination into a higher; as, to bring farthings into pence, or shillings into, pounds.

REDUCTION DESCENDING.

EXAMPLE.

1. In 48£. 12s. 7d. 2 qr., how many farthings?

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