John bought a rectangular doormat that was 1/2 a meter long and 3/10 a meter wide. suppose the doormat has a design on it that divides it into squares measuring one 1/10m by 1/10m how many squares is the doormat divided into?

We can find the area of the doormat, in square meters, by multiplying 1/2 and 3/10, getting 3/20.  Each square is 1/10*1/10=1/100 square meters.

(3/20)/(1/100) will give the ratio of the size of the doormat to the size of the squares, and thus the amount of squares needed.  This is equal to 15 squares, so the doormat will be divided into 15 squares.