



 
This follows from two of the properties of addition and multiplication, first the distribution of multiplication over addition. \[\mbox{If a, b, and c are any real numbers then } a(b + c) = ab + ac.\] The second property is that the number 1 is a multiplicative identity. \[\mbox{If a is any real number then } a\times 1 = 1 \times a= a.\] Using the fact that 1 is a multiplicative identity \[P + Pr = P \times 1 + P \times r.\] Now since multiplication distributes over addition \[P \times 1 + P \times r = P \times (1+r) = P(1+r).\] For your second expression first write \[P/P + Pr/P = P \times \frac{1}{P} + Pr \times \frac{1}{P}.\] Harley 



Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 