### The distributive law – multiplication over addition

3 (2 + 4) = 3 × 2 + 3 × 4

More generally,

*a* × (*b* + *c*) = (*a* × *b*) + (*a* × *c*) for any numbers *a*, *b* and *c*.

We use the distributive law to simplify some multiplication problems. We will return to consider more of these when we consider the distributive law for multiplication over subtraction.

For example:

- 7 × 101 = 7 × (100 + 1) = 700 + 7 = 707
- 7 × 102 = 7 × (100 + 2) = 700 + 14 = 714.