SUBTRACTION OF DENOMINATE NUMBERS. 83. IF we wish to subtract £15 13s. 10d. from £20 5s. 8d., we proceed as follows: OPERATION. £ S. d. 20 5 8 15 13 10 4 11 10 We place the numbers of the subtrahend directly under the numbers of the same denomination in the minuend, and draw a line underneath. Commencing with the pence, we see that we cannot subtract 10d. from 8d.; we therefore increase the 8d. by 12d. making 20d.; then subtracting 10d. from the 20d., we have the difference 10d., which we write under the column of pence. Having added 12d. to the minuend, we must equally increase the subtrahend, which we do by adding 1s. (the same as the 12d.,) to the 13s., making 14s. This cannot be subtracted from 5s.; we therefore increase the 5s. by 20s., making 25s. Now, subtracting 14s. from 25s. we have 11s., which we write under the column of shillings. Before subtracting the pounds, we add £1 to £15 to compensate for the 20s. added to the 5s., and then say £16 from £20 leaves £4. NOTE. It will be seen that this process is similar to that in the "shorter and more practical" example of simple subtraction, (ART. 12.) But the preceding subtraction might be also performed as in the second example of simple subtraction. Hence, we have this general RULE I. Place the less number under the greater, so that the same denominations may stand under each other; draw a line below them. II. Begin at the right, and subtract each number in the lower line from the one directly above it, and set the remainder below. III. If any number in the lower line is greater than the one above it, add so many to the upper number as make one of the next higher denomination; then subtract the lower number from the upper one thus increased, and set down the remainder. Carry 1, expressing the increase of the upper line, to the next number in the lower line; after which subtract this number from the one above it, as before; and thus proceed till all the numbers are subtracted. PROOF. If the work be right, the difference added to the subtrahend will equal the minuend; as in simple subtraction. |