In previous topics, Multiplying numbers near 100 – Part 1 and Multiplying numbers near 100 – Part 2, we studied how to multiply numbers which are near base 100, on either side of it. The same method can be extended higher bases of 10, i.e. 1000, 10000 and so on.

Here, we are going to learn how to multiply large numbers, which are near 1000.

Again, there are 2 parts of the answer, left part (which is most significant part) and right part (which is least significant part). The figures on the right are obtained by finding how much is the number above or below 1000. If the number is above 1000, then figure is positive and if the number is below 1000, then figure is negative. To get right part of the answer, we multiply figures on the right *vertically. *And to get the left part of the answer, we add the 1st number crosswise with 2nd figure or 2nd number crosswise with 1st figure.

Note: The number of spaces needed on the right is the number of 0’s in the base number.

Let us understand this method with few examples.

Case 1: Numbers are below base 1000

674 x 998

674 is 326 below 1000

998 is 2 below 1000

Since 1000 has 3 zeroes, so there will be 3 digits in the right part.

To get right part, we multiply 2 figures on right vertically (-326) x (-2).

To get left part, we perform crosswise addition of 1st number with 2nd figure on right (672+ (-2)) or 2nd number with 1st figure on right (998 + (-326)).

Case 2: Numbers are above base 1000

1142 x 1004

1142 is 142 above 1000

1004 is 4 above 1000

Since 1000 has 3 zeroes, so there will be 3 digits in the right part.

To get right part, we multiply 2 figures on right vertically (142 x 4).

To get left part, we perform crosswise addition of 1st number with 2nd figure on right (1142 + 4) or 2nd number with 1st figure on right (1004 + 142).

Case 3: Numbers are on either side of base 1000

1232 x 996

1232 is 232 above 1000

996 is 4 below 1000

Since 1000 has 3 zeroes, so there will be 3 digits in the right part.

To get right part, we multiply 2 figures on right vertically (232 x (-4)).

To get left part, we perform crosswise addition of 1st number with 2nd figure on right (1232 + (-4)) or 2nd number with 1st figure on right (996 + 232).

This method can be extended in similar fashion to multiplication of numbers when we have carry or borrow.

With this method, we can multiply any pair of numbers which are close to base 1000; For example: 1112 x 1005, 1213 x 1007, 1111 x 1004, 1402 x 988, 1413 x 991, 978 x 896, 971 x 972 etc.