Grid method
From Wikipedia, the free encyclopedia
The grid method is a form of long multiplication using a Partial Products Algorithm. Traditional long multiplication of, for instance, 26 x 13, would be written like this:
26 13 -- 78 260 --- 338
Using the grid method, 26 x 13 would look like this:
| x | 20 | 6 |
| 10 | 200 | 60 |
| 3 | 60 | 18 |
200 60 60 18 --- 338
The grid method differs in clearly breaking the multiplication and addition into two steps, and in being less dependent on place value.
In recent years it has become very common in primary schools in England. While it is less efficient than the traditional method, it is considered to be more reliable, in that children are less likely to make mistakes. Since anyone doing a lot of multiplication would use a pocket calculator, efficiency is less important nowadays; equally, since this means most children will use the multiplication algorithm less often, a more explicit (hence memorable) method is useful.
The grid method is of course simply an implementation of the distributive law that a(b+c) = ab + ac, and can be used in other contexts where it is easier to find a product by breaking it down, eg 21⁄2 x 11⁄2
| x | 2 | 1⁄2 |
| 1 | 2 | 1⁄2 |
| 1⁄2 | 1 | 1⁄4 |
2 + 1 + 1⁄2 + 1⁄4 = 33⁄4
Or (a + 3)(b + 2)
| x | a | 3 |
| b | ab | 3b |
| 2 | 2a | 6 |
ab + 3b + 2a + 6
