By the practice of
addition the eye and mind soon become accustomed to act rapidly, and
this is the art of addition. Grouping figures together is a valuable
aid in rapid addition, as we group letters into words in reading.
862 \
538 /
674 \
843 /
____
2917
Thus, in the above example, we do not say 3 and 4 are 7 and 8 are 15
and 2 are 17, but speak the sum of the couplet, thus 7 and 10 are 17,
and in the second column, 12 and 9 are 21. This method of grouping
the figures soon becomes easy and reduces the labor of addition about
one-half, while those somewhat expert may group three or more figures,
still more reducing the time and labor, and sometimes two or more
columns may be added at once, by ready reckoners.
Another method is to group into tens when it can be conveniently done,
and still another method in adding up long columns is to add from the
bottom to the top, and whenever the numbers make even 10, 20, 30, 40
or 50, write with pencil a small figure opposite, 1, 2, 3, 4 or 5, and
then proceed to add as units. The sum of these figures thus set out
will be the number of tens to be carried to the next column.
6^{2} 2 8
3 5^{2} 4^{1}
2 8 4
9 6 2
7^{2} 1 8^{2}
8 3^{2} 5
5 2 7
1^{1} 3 2^{1}
5 8 8
_________________
5 0 2 8
SHORT METHODS OF MULTIPLICATION.
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