In the topic “Proportionately – Part 1“, we studied the cases when the numbers multiplied were multiples or ratio of base numbers (near to the base of 10s, i.e. 10, 100, and so on).

There is a special case of Proportionately for the numbers multiplied when the left-most digit (most significant digit)  of the numbers are the same.

This is more useful when the numbers are near base of 10s (i.e. 10, 100, and so on).

For example:

214 x 204

Here left-most digit is 2 for both the numbers, i.e. place value of 2 is 200 which is closer to base 100.

So, we will use the similar method that we learnt earlier in different topics under “Base multiplications”. The only difference is we multiply the left part with 2 as the number is near twice base of 100.

proportionately 3

Another example where we have carry:

27 x 29

Here left-most digit is 2 for both the numbers , i.e. place value of 2 is 20 which is closer to base 10. We multiply the left part with 2 as the number is near twice base of 10.

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You can use this method to solve below problems:

42 × 44                    205 × 217                   322 × 304                   203 × 208
902 × 909                48 × 47                       188 × 196                   199 × 198