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In this article, we shall discuss the Vedic Math sutra "vertically and crosswise". This is the General Formula which is applicable to all the cases of multiplication. You will found this method very useful in division also that we shall discuss later. In the previous sutras, you subtracted crosswise; now you will multiply crosswise.
A. Multiplication of two digit numbers
For ab x uv
The numbers are written from left to right.
Now multiply:
1) vertically (a x u)
2) crosswise in both directions and add (a x v) + (b x u)
3) vertically (b x v)
The answer has the form: au | av + bu | bv
Following is the example of two-digit multiplication will make this clear:
12 x 23
1 2
2 3
--------------
2 | 3 + 4 | 6
= 2 | 7 | 6
= 276
The previous examples involved no carry figures, so let us consider this case in the next example.
64 x 93
6 4
9 3
-----------------
54 | 18 + 36 | 12
=54 | 54 | 12
=54 | (54 + 1) | 2 (Carry over the 1)
=54 | 55 | 2
=(54 + 5) | 5 | 2 (Carry over the 5)
=59 | 5 | 2
64 x 93 =5952
The Algebraic Explaination is:
Let the two 2 digit numbers be (ax+b) and (ux+v). Note that x = 10. Now consider the product
(ax + b) (ux + v)
= au. x2 + avx + bux + b.v
= au. x2 + (av + bu)x + b.v
The first term i. e. the coefficient of x2 is got by vertical multiplication of a and u
The middle term i. e. the coefficient of x is obtained by the cross-wise multiplication of a and v and of b and u and the addition of the two products
The independent term is arrived at by vertical multiplication of 'b' and 'v'
In this article, we shall discuss the Vedic Math sutra "vertically and crosswise". This is the General Formula which is applicable to all the cases of multiplication. You will found this method very useful in division also that we shall discuss later. In the previous sutras, you subtracted crosswise; now you will multiply crosswise.
A. Multiplication of two digit numbers
For ab x uv
The numbers are written from left to right.
Now multiply:
1) vertically (a x u)
2) crosswise in both directions and add (a x v) + (b x u)
3) vertically (b x v)
The answer has the form: au | av + bu | bv
Following is the example of two-digit multiplication will make this clear:
12 x 23
1 2
2 3
--------------
2 | 3 + 4 | 6
= 2 | 7 | 6
= 276
The previous examples involved no carry figures, so let us consider this case in the next example.
64 x 93
6 4
9 3
-----------------
54 | 18 + 36 | 12
=54 | 54 | 12
=54 | (54 + 1) | 2 (Carry over the 1)
=54 | 55 | 2
=(54 + 5) | 5 | 2 (Carry over the 5)
=59 | 5 | 2
64 x 93 =5952
The Algebraic Explaination is:
Let the two 2 digit numbers be (ax+b) and (ux+v). Note that x = 10. Now consider the product
(ax + b) (ux + v)
= au. x2 + avx + bux + b.v
= au. x2 + (av + bu)x + b.v
The first term i. e. the coefficient of x2 is got by vertical multiplication of a and u
The middle term i. e. the coefficient of x is obtained by the cross-wise multiplication of a and v and of b and u and the addition of the two products
The independent term is arrived at by vertical multiplication of 'b' and 'v'
