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COMPOUND SUBTRACTION.

Compound Subtraction teaches to find the difference between two numbers of several denominations.

RULE.

1. Place the less number under the greater, so that those of the same denomination may stand directly under each other, and draw a line below them.

2 Beginning at the lowest denomination, take each figure in the lower line from that above it, and set down the remainder.

3. But if the lower denomination be more than that above it, add as many as make one of the next greater denomination to the upper number; then subtract, and set down the remainder, as before.

4. Proceed to the next greater denomination, paying the one you borrowed, as in simple subtraction; thus continue through every denomination to the last.

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In the first example, beginning at the denomination of farthings, I say, 1 from 3, there remain 2, which I set down; then, in the denomination of pence, I find 8 cannot be taken from 7, therefore I borrow 1 shilling, or 12 pence, and add them to 7, the upper figure, which make 19, from which I subtract 8, and the remainder 11 I set down; then proceed, saying, 1 that I carry and 14 are 15; 15 from 18, there remain 3, which being set down, I proceed to the last place, and subtract as in whole numbers.

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Reduction teaches to bring numbers from one denomination to others of different denominations retaining the same value.

Reduction is of two kinds-DESCENDING, and AsCENDING; the former of which is performed by mul tiplication, the latter by division.

Reduction Descending.

RULE.

Multiply the highest denomination given, by so many of the next less, as make one of the greater; so continue 'till you have reduced it as low as you desire.

If the given number consist of several denominations, remember to add in the numbers in each de nomination, as you reduce the highest to them.

EXAMPLES.

1. Reduce .182 to farthings.

£. 182

Multiply by 20 the shillings in a pound.

by

by

3640 the shillings in £.182.

12 the pence in a shilling.

43680 the pence in £.182.

4 the farthings in a penny.

Answer, 174720 the farthings in £.182.

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