29 Apr 2013

Fun With Maths - Part 3 - The Bush Calculator

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=8 000.
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.
Total=5 002.

Who said Maths was difficult? We only need to know our 10 times, hundred times, thousand times and ten thousand times tables.


1 comment:

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