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Multiplication using Multibase Arithmetic Blocks

A child can be taught the multiplication algorithms using MAB. The use of these blocks is illustrated with examples.

Click below to see the following examples.

| Multiplication by ones | Multiplication by tens |

Multiplication by ones

Example 1: 3 X 6

Three groups of 6 will be as shown below.

Now there are more than 10 blocks.

10 of these can be traded for one long or ten.

So the answer is 18.

Example 2: 23 X 4

23 is represented by

4 groups of 23 will be

Now there are 8 longs and 12 ones.

At this stage, 10 ones can be traded for 1 long, giving 9 longs and 2 ones.

4 groups of 23 become 9 longs and 2 ones, giving 92.

Multiplication by 10

Understanding how numbers move into adjacent place value columns when multiplied by ten is a crucial fact underlying the multiplication algorithms. The formal algorithms are built from this basic information.

Example 3: 10 X 2

Start with 10 groups of 2

10 ones can be traded for a long and then the other 10 ones can be traded for another long.

Thus 10 groups of 2 become 2 tens or twenty.

Example 4: 10 X 32

32 is 3 tens and 2 ones.

That is 3 longs and 2 ones.

10 groups of 32 will be

Now there are 30 longs and 20 ones.

10 longs can be traded for a flat.

30 longs can be traded for 3 flats.

And the 20 ones can be traded for 2 longs.

So in all we have 3 flats and 2 longs.

The answer is 320.