42x43
The area of a region is the sum of the areas of its
non-overlapping parts. How can we use this postulate to demonstrate that this
block illustrates the traditional way to multiply 42 by 43? The blue block has
dimensions of 40 by 40, making it a square. The green blocks below the 40x40
block are the dimensions 40x1, as are the other green blocks next to the 40x40
block. The yellow blocks represent 1x1 squares. Before demonstrating how the
blocks illustrate the equation, take the equation 42 x 43 and multiply it.
First multiply 2 and 3. 2x3=6
Next multiply 3 by 40. 3x40= 120
Now multiply 2 by 40. 2x40=80
Finally, multiply 40 and 40. 40x40= 1600
6+120+80+1600= 1806
This is how one would traditionally multiply 43 by 42. You
would line the numbers up and multiply the top by the bottom. Now, multiply the
area of the blocks. The area of a rectangle is equal to the base multiplied by
the height. Taking this equation, find the areas of each block.
Yellow blocks with 1x1 dimensions: 3 blocks across x 2 blocks down= 2 x 3=6
Green blocks on right with 1x40 dimensions: 3 blocks across=
3 x 40=120
Green blocks on bottom with 1x40 dimensions: 2 blocks down= 2 x 40= 80
Blue block with 40x 40 dimension: 1 block= 40
x 40= 1600
6+120+80+1600= 1806
Multiplying 42 x 43 and calculating the area of the blocks
both yield an answer of 1806. The block method even parallels the
multiplication because the exact same equations are performed to find the answer.
How does this work? It is important to remember that when you multiply a
number, you are saying “it is this number this many times”. The blocks
illustrate this idea. You take the block with 1x40 dimensions and you say “it
is 1x40 three times because there are three blocks”. The dimensions of the
block are 42x43 (the blue block plus two green blocks down and the blue block
plus three green blocks across), but you are just dividing the area further so
that you can work with more manageable numbers.
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