SUBSTRACTION

, or Subtraction, in Arithmetic, is the taking of one number or quantity from another, to find the remainder or difference between them; and is usually made the second rule in arithmetic.

The greater number or quantity is called the minuend, the less is the subtrahend, and the remainder is the difference. Also the sign of Subtraction is -, or minus.

Subtraction of Whole Numbers, is performed by setting the less number below the greater, as in addition, units under units, tens under tens, &c; and then, proceeding from the right hand towards the lest, subtract or take each lower figure from that just above, and set down the several remainders or differences underneath; and these will compose the whole remainder or difference of the two given numbers. But when any one of the figures of the under number is greater than that of the upper, from which it is to be taken, you must add 10 (in your mind) to that upper figure, then take the under one from this sum, and set the difference underneath, carrying or adding 1 to the next under figure to be subtracted. Thus, for example, to subtract 2904821 from 37409732

To prove Subtraction: Add the remainder or difference to the less number, and the sum will be equal to the greater when the work is right.

Subtraction of Decimals, is performed in the same manner as in whole numbers, by observing only to set the figures or places of the same kind under each other. Thus:

To Subtract Vulgar Fractions. Reduce the two fractions to a common denominator, if they have different ones; then take the less numerator from the greater, and set the remainder over the common denominator, for the difference sought.—N. B. It is best to set the less fraction after the greater, with the sign (-) of subtraction between them, and the mark of equality (=) after them.

Thus,

, in Algebra, is performed by changing the signs of all the terms of the subtrahend, to their contrary signs, viz, + into -, and - into +; and then uniting the terms with those of the minuend after the manner of addition of Algebra.