Shortcut Method for Multiplication

A guest post by Nandeesh H.N. of Kolkata

Shortcut multiplication for approximate numbers

When applying the rules of multiplication of exact numbers to approximate numbers we waste time and effort in the computation of digits that will be dropped at a later stage. The computation can be made more efficient if we are guided by the following rules:


1.      Equalize the number of significant digits of multiplicand and multiplier. In case of 6.7428 * 23.45, round off 6.7428 as 6.743 to make four significant digits as in 23.45.

2.      Start the multiplication with the higher digit places of the multiplier (not the lower digit places).  In case of 6.743 * 23.45, the multiplier is 23.45 and we have to start the multiplication with 2 and not 5.

3.      Before multiplication by the next place of the multiplier, cross-line the last digit of the multiplicand. (i.e.  3 of 6.743). That is, multiply 6.74 with 3 of 23.45. However, add to the result the rounded product of 3 of 23.45 by the discarded digit 3 of 6.743.

4.      Before multiplication by the next place of the multiplier, cross-line the last digit of the multiplicand. (i.e.  4 of 6.74). That is, multiply 6.7 with 4 of 23.45. However, add to the result the rounded product of 4 of 23.45 by the discarded digit 4 of 6.74. And so on.

5.      The resulting products are arranged so that all lower order digits are arranged one under another.

6.      Place the decimal point as per the rough estimate of the result.

Example:
6.7428 * 23.45
6.743 * 23.45  (Round off 6.7428 as 6.743)
—————-
13486   (6743 * 2 = 13486. Strike out 3 of 6.743)
2023  ( 6743 * 3 = 20229 which is written as 2023 for 674 * 3. Strike out 4 of 674)
270 ( 674 * 4 = 2696 which is written as 270 for 67 * 4. Strike out 7 of 67)
34        ( 67 * 5 = 334 which is written as 34 for 6 * 5.)
———-
158.13  (Place the decimal considering 7 * 23 is about 158)
158.1   (Rounding off the result to four significant digits)
———

Example:
96.538 * 73.64
96.54 * 73.65   (Round off 96.538 as 96.54)
—————-
67578   (9654 * 7 = 67578. Strike out 4 of 9654)
2896  ( 9654 * 3 = 28962 which is written as 2896 for 965 * 3. Strike out 5 of 965)
579 ( 965 * 6 = 5790 which is written as 579 for 96 * 6. Strike out 6 of 96)
48        ( 96 * 5 = 480 which is written as 48 for 9 * 5.)
———-
7110.1  (Place the decimal considering 97 * 74 is about 7110)
7110    (Rounding off the result to four significant digits)
———-

This post is contributed by Nandeesh Nagarajaia. He is a Chemical Engineer who did his B.Tech from NIT Suratkal.  He is now in IT field as Assistant General Manager(Systems) in Hindustan Copper Limited. He love Maths and enjoy teaching Maths to his sons.

On behalf of all the QuickerMaths.com users, I  am highly grateful for his contribution.

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