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RULE. Write all the given numbers so that units of the same denomination may stand in the same column.

Add as in addition of simple numbers; and carry, from column to column, one for as many units as it takes of the denomination added to make a unit of the denomination next higher.

Proof. — The proof is the same as in addition of simple numbers.

EXAMPLES FOR PRACTICE.

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APOTHECARIES' WEIGHT. 4.

5. 10 3 Э gr.

Ib Z 3

gr. 81 11 6 1 19

35 9 6 2 19 7 5 10 7 2 13

71 1 1 1 11 14 9 7 1 12

37 3 3 2 1 2 37 8 1 1 11

14 4 7 1 13 61 11 3 2 3

75 5 6 1 17

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oz.

AVOIRDUPOIS WEIGHT. 6.

7. T. cwt. qr. lb.

dr.

T.
cwt. qr.

lb.

OZ. dr. 71 19 3 17 14 13 14 13 2 15 15 15 14 13 1 11 13 12 13 17 3 13 11 13 39 9 3 13 9 9 46 16 3 11 13 10 15 17 3 16 10 14 14 15 2 7 6 9 61 16 3 13 7 8 11 17 3 10 15 11

203 17 3 2 3

8

8

QUESTIONS. – What is the rule? The proof?

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m.

deg. 18

19 61 47 78 32 17 59 28 56

0 0

LONG MEASURE. 10.

11. fur. rd. ft. in.

fur. rd. yd. ft. in. 7 15 11 1 12 7 35 5 2 11 6 39 10 11 13 6 15 3 1 10 5 14 9 9 16 1 17 1 2 5 7 36 16 10 13 4 13 2 1 9 1 30 16 1 17 7 36 5 2 7

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m.

205 9 1 17 15 2

SURVEYORS' MEASURE. 12.

13. fur. ch. p. 1.

m. fur. ch. p. 1. 17 5 8 3 24

14 7 9 3 21 16 3 7 1 21

37 1 0 3 16 47 7 9 3 19

17 7 8 3 17 19 6 6 1 16

61 6 5 3 16 31 7 1 0 20

47 1 1 0 2 3

15.

133 7 4 0 0

SQUARE MEASURE.

14.
A. R.
p. ft.

in.
A. R.
p. yd.

in. 67 3 39 272 143 43 1 15 30 8 17 78 3 14 260 116 16 3 39 19 7 141 14 2 31 167 135 47 1 16 27 5 79 67 1 17 17 6 131 38 3 17 18 8 17 49 3 31 69 117

15 1 32 11 i 117

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SOLID MEASURE.

16. Tun. ft.

in. 17 39 1371 61 17 1711 47 16 16 6 6 71 38 1711 47 17 1617

246 11 1164

WINE MEASURE. 18. Tun. hhd. gal. qt. pt. 61 1 6 2 3 1 71 3 14 1 1 6 0 0 17 3 0 14 1 51 1 1 57 3 14 3 1

2 6 5

2 3 5 1

0

BEER MEASURE. 20. Tun. hhd. gal qt. pt. 15 3 5 0 3 1 67 3 17 3 1 17 1 44 1 0 71 3 12 3 1 81 1 18 1 0

254 1 3 6 0 1

DRY MEASURE.

ch. 15 01 51 42 14

22. bu. pk.

qt. pt. 35 3 7 1 16 3 6 1 30 1 5 0 17 2 2 1 14 1 4 1

186

17. Cord. ft. 14 116 1169 67 113 1711 96 127 969 19 98 1376 14 37 1414

19. Tun. hhd. gal. qt. pt. 14 3 18 3 0 81 1 60 3 1 17 3 61 3 0 61 3 5 7 3 1 17 1 17 1 0

21. Tun. bhd. gal. qt. pt. 67 1 51 1 0 15 3 16 3 1 44 1 4 5 1 1 15 2 12 2 1 67 3 35 1 0

23. ch. bu. pk. qt. pt. 71 17 1 1 1 16 31 3 3 0 41 14 3 1 1 71 17 1 0 1 10 10 2 3 0

7 1 2 0

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NOTE. — The sum of the signs, in circular motion, must_always be divided by 12, and the remainder only be written down, as in Ex. 26.

♡ XII. SUBTRACTION OF COMPOUND NUMBERS.

Art. 102. SUBTRACTION of Compound Numbers is the process of finding the difference between two compound numbers.

ENGLISH MONEY.
Ex. 1. From 87£. 9s. 6d. 3far., take 52£. 11s. 7d. 1far.

Ans. 34£. 178. 11d. 2far.
OPERATION

Having placed the less number under £. . d.

the Min. 87 9 6 3

greater, farthings under farthings, Sub. 5 2 11

pence under pence, &c., we begin with 7 1

the farthings, thus : 1 far. from 3 far.

leaves 2 far., which we set under the Rem. 34 17 11 2 column of farthings. As we cannot

far.

QUESTIONS. — Art. 102. What is subtraction of compound numbers? How do you arrange the numbers for subtraction ?

take 7d. from 6d., we add 12d. = ls, to the 6d., making 18d., and then subtract the 7d. from it, and set the remainder, Ild., under the column of pence. We then add ls. 12d. to the lls. in the subtrahend, making 128., to compensate for the 12d. we added to the 6d. in the minuend. (Art. 30.) Again, since we cannot take 128. from 98., we add 20s.=1£. to the 98., making 29s., from which we take the 12s., and set the remainder, 178., under the column of shillings. Having added 1£. = 20s. to the 52£., to compensate for the 20s. added to the 98. in the minuend, we subtract the pounds as in subtraction of simple numbers, and obtain 34£. for the remainder, and as the result complete, 34£. 178. 11d. 2far.

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 denomination before subtracting, and carry one to the next lower number before subtracting it.

PROOF. - The proof is the same as in simple subtraction.

EXAMPLES FOR PRACTICE. 2.

3. £. s. d. far.

£.

d. far 78 11 5 2

765 16 10 1 41 13 3 3

713 17 11 3

8.

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5 3 14 17

APOTHECARIES' WEIGHT.
6.

7.
3
gr.

gr. 7 1 2 15

161

1 17 11 9.7 1 19

9 7 7 1 2 18

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3 9 2 0 16

QUESTIONS. - What do you do when the upper number is smaller than the lower ? How many do you carry to the next denomination? What is the rule for subtraction? The proof?

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