SMMG
The Lost Art of Computation
April 11, 2015
Begin with these warm-up exercises. Make sure that you add left to right to practice working in that direction rather
than right to left.
2
6
C
1
2
2
3
2
1
0
9
C 3
1
6
8
9
0
C
3
1
3
5
6
2
C
8
0
4
C
1
5
4
5
6
8
2
1
2
2
2
1
5
6
4
C
1
6
0
7
C
7
3
2
2
1
7
7
4
2
3
8
0
1
1
7
2
Question to consider: why is it just as easy to add these particular examples from left to right as it is to add them from
right to left?
1
Now complete these exercises, again adding from left to right without carrying anything.
7
6
C
5
2
9
2
9
9
4
C 6
7
1
9
6
C
7
6
5
5
C
2
7
6
C
3
2
5
8
4
6
7
8
8
4
9
1
5
4
7
9
5
2
4
9
4
1
5
5
3
1
3
3
4
5
5
2
1
8
4
8
6
7
6
0
9
3
5
8
3
2
3
3
4
2
C
C
5
1
6
8
C
9
7
5
7
9
9
9
9
9
9
1
0
0
0
0
1
Question to consider: when adding two numbers only (not many as in the last example above), can a number ever be
underlined twice?
2
Start the subtraction section with these warm-up exercises. As with addition, make sure that you subtract from left to
right.
2
6
7
8
3
8
5
4
2
7
2
9
1
2
4
2
0
1
0
4
1
6
0
4
8
2
2
8
5
6
9
3
7
9
4
5
3
8
9
1
2
7
6
1
0
3
4
1
6
2
4
4
1
3
1
5
1
0
0
2
Question to consider: why is it just as easy to subtract these particular examples from left to right as it is to add them
from right to left?
3
Now complete these exercises, again subtracting from left to right without borrowing anything.
7
5
7
6
6
7
6
9
1
5
8
4
8
6
8
3
9
5
5
7
6
1
5
2
9
9
4
8
4
6
7
3
8
9
0
0
0
0
0
1
7
1
9
6
4
9
1
5
7
7
1
0
0
0
0
1
Question to consider: must a number ever be slashed twice to indicate a reduction by 2 instead of 1?
4
Try using the Russian Peasant method of multiplication to find the following products.
89 53
72 89
268 373
(Hint: which numbers do you want to double and which do you want to halve?)
5
Use the lattice method to find 9382 3847.
6
Use your Napier’s Bones to find the following products.
89 53
72 89
373 268
Did you find this easier or harder than the Russian Peasant method? For a challenge, use Napier’s Bones to find
47963 243.
7
Try finding 7524 2859 using each of the following methods:
1) the standard right-to-left method of multiplying and carrying
2) the left-to-right method without carrying
3) Napier’s Bones
4) lattice multiplication
8