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75. I am indebted to A, 107. 11s. 6d.; to B, 29l. 198. Od. ; to C, 1291. Os. 11d.; to D, 3795l. 18s. 10d.; to E, 7891. 19s. 9d. ; and to F, 2391. 19s. 8d.4; what sum do I owe in all. Ans. 49951. 9s. 10d.4.

76. A poor widow received in charitable donations as follows; viz. from F, ten guineas; from G, three moidores: from H, one hundred pounds; from K, fifty shillings; from T, eleven crown pieces; from X, seventeen guinea notes; and from Z, a check on his banker for threescore and ten pounds; what did she receive in all. Ans. 2071. 13s.

77. What does my house stand me in per year, supposing the rent is forty pounds ten shillings; the assessed taxes, fifteen guineas and sixpence; land tax, three pounds five shillings; poor's rate, six pounds seven and fourpence; and church rate, highway rate, &c. two guineas and a half? Ans. 681. 10s. 4d.

78 A silversmith sold plate as follows; on Monday he sold 7lb. 11oz. 19dwts. 17gr.; on Tuesday, 12lb. 10oz. 17dwts. 23gr.; on Wednesday, 9lb. 11oz. 12dwts. 20gr.; on Thursday, 157b. 11oz. 14dwts. 21gr.; on Friday, 23lb. 9oz. 17dwts. 15gr.; and on Saturday, 117b. 10oz. 13dwts. ; what quantity did he sell during the whole week? Ans. 82lb. 6oz. 16dwts.

79. A wholesale grocer sent the following quantities of sugar to five customers; viz. to A, 3cwt. 3qr. 271b.; to B, 5cwt. Qqr. 26lb.; to C, lcwt. 2qr. 2lb.; to D, 4cwt. 3qr. 25lb.; and to E, 3qr. 26lb.; what quantity did he send in all ? Ans. 17cwt. 22lb. 80. A person bought six pieces of Irish linen; the first containing 7yds. 3qr.; the second, 19yds. 3gr. 3n.; the third,

28yds. 3qr. 2n.; the fourth, 33yds. 2qr.; the fifth, 6yds. 2qr. 3n.; and the sixth, 10yds. 3qr. 3n.; what was the whole quantity bought? Ans. 107yds. 2qr. 3n.

81. A common was ordered to be inclosed, and it was accordingly divided into 6 meadows; the first containing 27a. 3r. 31p.; the second, 14a. 3r.; the third, 32a. 2r. 25p.; the fourth, 15a. 3r. 18p.; the fifth, 32a. 1r. 19p.; and the sixth, 3r. 39p.; there were also 12a. 2r. 11p. allotted for a road through the ground; what quantity of land did the common contain? Ans. 137a. 23p.

82. A farmer bought several quantities of wheat as follows; of A he bought 3ld. 2gr. 5bu.; of B, 3qr. 7bu. 3pk.; of C, 11ld. 1qr.; of D, 7bu. 3pk.; of E, 4qr. 6bu. 3pk.; and of F, 14ld. 4qr. 3pk.; how much did he buy in all? Ans. 31ld. 2gr. 4bu.

83. A coal-merchant received five lighters loaded with coals from the pool; the first contained 12ch. 3bu. 3pk.; the second, 19ch. 27bu. 3pk.; the third, 17ch. 35bu. 2pk.; the fourth 11ch. 29bu. 3pk.; and the fifth, 23ch. 32bu. 3pk.; how many chaldrons did he receive? Ans. 85ch. 21bu. 2pk.

COMPOUND SUBTRACTION.

76. Compound Subtraction teaches to find the difference of two given compound numbers of the same kind, by taking the less from the greater.

RULE. Place the less compound number below the greater, so that like denominations may stand under each other as in Compound Addition.

Beginning at the least denomination, subtract the lower numbers from those above, putting each remainder under its respective denomination.

When the lower number of any denomination is greater than the upper, increase the upper by as many as make one of the next superior denomination, subtract the lower number from this sum, set down the remainder, and carry 1 to the next lower number; subtract, and proceed in this manner until the work is finished.

e When the inferior denominations in the upper line are respectively greater than those in the lower, the reason of the rule is plain; when they are less, the borrowing and carrying depend on the same principles as common subtrac

Method of Proof.

Add the remainder (or number arising from the operation) and the lesser number together, and if the sum be like the greater, the work is right.

EXAMPLES.

1. From 1237. 4s. 5d. take 102l. 19s. 6d.

OPERATION.

L.
123 4

S.

102 19

Rem.

20 4

d. 5/1/

Explanation.

Here I begin at the farthings, and say, 3 from 1 I cannot, I therefore borrow 4 farthings, which added to the I make 5, then 3 from 5, and 2 remain; put down, and carry 1 to the 66 makes 7; then I say, 7 from 5 I cannot, bor10/1/ row 12 to the 5 which make 17, then 7 from 17, and 10 remain; put down 10, and carry 1 to 19 make 20; then 20 from 4 I cannot, therefore I borrow 20 to the 4, making 24, then 20 from 24, and 4 remain; put down 4, and carry 1 to the 2: the rest is merely simple subtraction. The proof arises from adding the remainder and the line next above it together by Compound Addition.

Proof 123 4

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tion does; so in Ex. 1. we borrow 4 (or 1 penny) in farthings, to compensate which we carry 1 (penny) to the pence; we borrow 12 (or 1 shilling) in pence, to compensate which we carry 1 (shilling) to the shillings; and in shillings we borrow 20, (or 1 pound,) carrying 1 afterwards to the pounds. That these carryings always exactly compensate for the number borrowed appears plain, for carrying I to the lower number is in effect the same as taking from the upper the 1 borrowed. The same reasoning may be applied to every kind of examples that can be proposed under this rule.

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