The formal statement of the distributive law should read as follows:
If a, b, c and d are numbers, or algebraic expressions (same thing really) and b = c + d then ab = ac + ad
It is a by-product of the law that it tells you how to expand an expression with a bracketed factor.
In any case, what’s the big deal ?
Let’s have a number line. We can count up or down by moving to the right or the left, or actually up or down if the number line is drawn vertically.
But what else ?????
The following pictures show how points on the number line which represent fractions can be found exactly by simple geometrical construction, and then how results of multiplication and division of fractions can be found exactly as points on the number line (sorry, the numerical values are however not found).
This arose from a statement in the CCSS math document that the fraction 1/6 could be represented by a point one sixth of the way from zero to one, BUT NOWHERE DOES IT SAY HOW TO FIND THAT POINT.