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| Math Central | Quandaries & Queries |
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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.. 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
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