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34. The Moon is 5S. 18° 14' 17" east of the Sun; Jupiter is 7S. 10° 29' 28" east of the Moon; Mars is 11S. 12° 11′ 56′′ east of Jupiter; and Herschel is 7S. 18° 38′ 15′′ east of Mars; how far is Herschel east from the Sun?

Ans. 7S. 29° 33′ 56′′.

SUBTRACTION OF COMPOUND NUMBERS.

146.

SUBTRACTION of Compound Numbers is the process of finding the difference between two compound numbers. Ex. 1. From 617£. 11s. 8d. take 181£. 15s. 5d.

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Ans. 435£. 16s. 3d.

Having placed the less number under the greater, pence under pence, shillings under shillings, &c., we begin with pence, thus: 5d. from 8d. leaves 3d., which we set under the

column of pence. As we cannot take

12. to

add 20s. from it, and set the Then, having added 20s. added to the 11s.

15s. from 11s., we the 11s., making 31s., and then subtract the 15s. remainder, 16s., under the column of shillings. 1£. = 20s. to the 181£., to compensate for the in the minuend, we subtract the pounds as in subtraction of simple numbers, and obtain 435£. for the remainder, and as the result complete, 435£. 16s. 3d.

RULE. Write the less compound number under the greater, so that units of the same denomination shall stand in the same column.

Subtract as in subtraction of simple numbers.

If any number in the subtrahend is larger than that above it, add to the upper number as many units as make one of the next higher denomi nation before subtracting, and carry one to the next lower number before subtracting it.

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The proof is the same as in simple subtraction.

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6 7 NOTE.

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As half a foot is equal to 6 inches, we add them to the 5 inches, which make 11 inches.

12. From 67yd. 1qr. 1na. lin. take 18yd. 2qr. 2na. 2in. Ans. 48yd. 2qr. 2na. 14in.

13. From 51E.E. 2qr. 3na. take 19E.E. 3qr. 1na. 14. From 56A. 1R. 19p. 119ft. 110in. take 17A. 3R. 13p. 127ft. 113in. Ans. 38A. 2R. 5p. 264ft. 33in.

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16. Subtract 19m. 2fur. 1ch. 3p. 211. from 21m. 1fur. 3ch. 2p. 191. Ans. 1m. 7fur. 1ch. 2p. 231. 17. From 28m. 6fur. 1ch. 2p. 181. take 15m. 7fur. 3ch. 1p. 191.

18. Required the value of 49T. 13ft. 1611in. 18T. 15ft. 1719in. Ans. 30T. 37ft. 1620in.

19. Required the value of 361C. 47ft. 1178in. 197C. 121ft. 1617in.

20. Subtract 11tun 1hhd: 28gal. 2qt. 1pt. from 79tun 3hhd. 19gal. 1qt. 1pt. Ans. 68tun 1hhd. 53 gal. 3qt.

21. Subtract of beer measure_191hhd. 19gal. 3qt. from 769hhd. 18gal. 1qt.

22. From 56ch. 2bu. 1pk. take 38ch. 3bu. 1pk.

Ans. 17ch. 35bu.

23. Required the value of 25bu. 3pk. 1qt. — 12bu. 3pk. 5qt. Ans. 12bu. 3pk. 4qt. 24. Required the difference between 6mo. 16d. 13h. 27m. 19s. and 1mo. 22d. 16h. 41m. 37s.

Ans. 4mo. 23d. 20h. 45m. 42s. 25. From 48y. Omo. 15d. 19h. 27m. 31s. take 19y. 10mo. 29d. 21h. 38m. 56s.

26. From 6S. 11° 12′ 48′′ subtract 9S. 8° 15' 56".

Ans. 9S. 2° 56′52′′.

27. Take 1S. 22° 19' 28" from 4S. 19° 41′ 22′′. 28. I have 73A. of land; if I should sell 5A. 3R. 1p. 7ft., how much should I have left? Ans. 67A. OR: 38p. 2651ft. 29. A owes B 100£.; what will remain due after he has paid him 3s. 6d. ? Ans. 99£. 16s. 54d.

30. 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. 31. Bought 7 cords of wood; 2 cords 78ft. having been stolen, how much remained?

32. I have 15 yards of cloth; having sold 3yd. 2qr. 1na., what remains? Ans. 11yd. 1qr. 3na. 33. 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. 20lb.

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

35. 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.

36. The Moon moves 13° 10′ 35′′ in a solar day, and the Sun 59′ 8′′; 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' 27".

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

Ans. 86bu. 1pk. Oqt. 1pt.

38. If from a stick of timber containing 2T. 18ft. 1410in. there be taken 38ft. 1720in., how much will be left? Ans. 1T. 19ft. 1418in.

MULTIPLICATION OF COMPOUND NUMBERS.

147. MULTIPLICATION of Compound Numbers is the process of taking a compound number any proposed number of times.

Ex. 1. What will 6 bales of cloth cost, at 7£. 12s. 7d. per bale? Ans. 45£. 15s. 6d.

OPERATION.

d.

£. 8.
12 7

Multiplicand 7
Multiplier

Product

6

=

Having written the multiplier under the lowest denomination of the multiplicand, we multiply thus: 7d. × 6 42d. 3s. 6d. We write the 6d. under the number multiplied, and reserve the 3s. to be added to the pro72s., and 3s. (carried) We write the 15s. under the column of shillings,

4 5

1 5 6

duct of the shillings. Then, 12s. X 6

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and reserve the 3£. to be added to the product of the pounds. Again, 7£. X 6 42£., and 3£. (carried) = 45£. This, placed under the column of pounds, gives 45£. 15s. 6d.

=

RULE. - Multiply each denomination of the compound number as in multiplication of simple numbers, and carry as in addition of compound

numbers.

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Proof. Write down by themselves the several products obtained by multiplying each denomination of the multiplicand by the multiplier, and these partial products added together will equal the entire product, if the work be right. (Art. 60.)

NOTE. — Going a second time carefully over the work is a good way of testing its accuracy. On learning Division of Compound Numbers, the pupil will find that rule a better method of proving multiplication of compound numbers.

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NOTE. The answers to the following examples may be found in corresponding numbers of examples in Division of Compound Numbers.

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9. Multiply 16A. 2R. 4p. 19yd. 7ft. 79in. by 11.

10. Multiply 10yd. 3qr. 3na. by 5.

11. Multiply 17tun 2hhd. 50gal. 1qt. by 7.

12. Multiply 29hhd. 61gal. 3qt. 1pt. 3gi. by 7.

13. Multiply 19bu. 2pk. 7qt. 1pt. by 6.

14. What is the value of 13y. 316d. 15h. 27m. 39s. × 8? 15. Multiply 16deg. 39m. 3fur. 39rd. 5yd. 2ft. by 9.

16. If a man gives each of his 9 sons 23A. 3R. 19дp., what do they all receive?

17. If 12 men perform a piece of labor in 7h. 24m. 30s., how long would it take 1 man to perform the same task?

18. If 1 bag contain 3bu. 2pk. 4qt., what quantity do 8 bags contain?

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