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Fun With Maths - Part
3 - The Bush Calculator - by P.K.Odendaal
So we are in the bush, and we quickly need to calculate the number
of stars in the night sky and our children are not there with their
calculators. What do we do?
We draw a few lines in the sand.
We need to multiply two double digit figures with each other.
Let's say 22 x 23 = 506.
We draw two thicker lines in the upper left and two thinner
lines in the lower right to represent 22.
We draw two thicker lines in the lower left and three
thinner lines in the upper right to represent 23.
Then we draw two dividing lines (red) as shown. These three
segments represent the 100's, 10's and 1's.
Now we count the crossings of the lines.
On the leftmost segment there are four crossings of the
thicker lines which this gives us 4x100=400.
There are ten crossing of the thick and thin lines in the
centre segment which gives us 10x10=100. Carry this 100 to the hundreds of 400
to give us 500. If there were only 9 crossing it would be 9x10=90. There is
nothing left in this segment. So it's 0.
There are six crossings of the thin lines giving us 6 x 1 = 6.
So the total is 506
But we need to calculate far larger figures.
In the next figure we are going to multiply 223 x 222 = 49 506
We now divide the lines into thick, medium and thin lines
and draw red lines (take a red soil) to divide the figure into five segments.
Starting from the left:
There are four thick crossings giving us 4 x 10 000=40 000.
Then we need to count the thick and medium line
intersections which is 8 in the second from left segment, giving us 8 x 1 000=8
Thirdly we look at the third segment from the left and count
the thin and medium line intersections, which is 14*100=1400. Carry the
thousand to the previous segment which gives us 9000 for that segment and 400
for this segment.
The fourth segment is the crossing of medium lines with thin
lines. There are 10 crossings giving us 10x10=100. Carry this 100 to the
previous hundreds total giving us 500. Zero is left in this segment.
The last segment on the right is the crossing of the thin
lines which is 6, giving us 6 x 1=6.
Total is 40 000 + 9 000 + 500 + 6 = 49 506.
Of course we will also have to multiply two digits with
three digits. Here we multiply 122 x 41 = 5 002
The first segment gives us 4 x 1000 = 4 000.
The second segment gives us 9 x 100 = 900.
The third segment gives us 10 x 10=100. Carry this over to
previous total which gives us 1000. Carry this 1000 of the second segment over
to the first segment total of 4 000 which gives us 5 000. The second and third
segments now have zero each.
The fourth segment gives us 2 x 1 = 2.
Who said Maths was difficult? We only need to know our 10
times, hundred times, thousand times and ten thousand times tables.