The Distributive Law : If you were asked to mentally multiply 37 with 9, how would you proceed? 1 would do it as follows - 37 is 30 + 7, 30 x 9 = 270, 7 x 9 = 63, so 270 + 63, that is, 270 + 60 + 3, i.e., 333 is the answer. You may do it by thiNting of 37 as 40 - 3, and then finding (40 x 9) - (3 x 9) as the answer. Or, you may do it directly by mentally visualising the algorithm.
Splitting a number up into parts helps us in efficient calculation. This way of calculating is possible because of the distributive law of multiplication with respect to addition / subtraction. What it says is that, for example,
(30 + 7) x 9 = (30 x 9) + (7 x 9)
More generally, for any three numbers a, b and c, the law says that
(a+ b) x c=(a x c) + (b xc), and
(a- b) xc=(axc)-(b xc).
How can we help children understand this law? Maya (see Example 2) told us what she does with the children of Class 3.