   SEARCH HOME Math Central Quandaries & Queries  Question from Kenneth: Hello P + Pr has a common factor of P so it can be expressed as P(1 + r) after the P is factored out.. How does the "P" get in front of (1 + r)? P/P + Pr/P = 1 + r What step is used to show that P is added in front of (1 + r)? I thank you for your reply. 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.