SUBTRACTION, SUBTRAHEND, MINUEND. The process of subtraction is the removal of a part equal to the peso from the greater. The quantity to be diminished (minitendum) was called the minuend ; the quantity to be withdrawn (subtrahendum), the subtrahend; and the remaining part, the remainder. The terms subtrahend and minuend are almost out of use, though often very convenient.
The operation of subtraction is often described in a way which might be practised, but is not; and the explanation of the possible mode applied to tho actual mode makes confusion. It is obvious enough that if parts of A be subtracted severally from greater parts of PI, the remainders put together make up the whole remainder. Thus, 24 can easily be taken from 76, for 7 tens exceeds 2 tens by 5 tens, and 6 exceeds 4 by 2, so that 52 is the remainder required. But when wo come to take 48 from 93, the preceding mode of partition is use less. To remedy this, it is proposed in the explanation to borrow I of the 9 tens in 94, and to put it on to the 4: then 8 from 13 leaves 5. Now take the 4 tens of 48, and subtract from the remaining 8 tens of 93, and 4 tens are left : the answer then is 45. The process would be
as follows : 93 8 from 3, impossible; borrow a ten from 00; 8 from 13 leaves 48 5. Take 4 teas from the remaining 8 tens, one of the 9 — tens having been borrowed, and 4 tens remain. 45 This process is actually used on the Continent ; but with us, as all tho world knows, there is a different process, as follows : 93 8 from 3 impossible ; take 8 from 13, and 5 remains. Carry* 49 one to 4, giving 5, and subtract 5 tens from 9 tens, giving 4 — tens.
45 There is quite a different principle in this process, which is as follows :—If two numbers be equally increased or equally diminished, the difference remains the same. Having arbitrarily increased the 8 in the upper line by 10, the lower line must be somewhere or other increased by 10, in order to keep the difference (which is all that is wanted) unaltered.
The object in view is attained by increasing the upper line by ten units, and the lower line by one ten.
For further detail, see COMPUTATION.