1/nb, (given b=1/150) answer is: 150/n. How??

Question

P = 1/nb + c

Given: b=1/150 and c = 17,000

The answer is: P= 150/n + 17,000, but how?

How do 1/(n*1/150) turn into 150/n?

Can someone please explain? Thank you!

Answer 1

You need the following properties:

• $\frac{a\cdot b}{c\cdot d} = \frac{a}{c}\cdot\frac{b}{d}$
• $1=1\cdot 1=1\cdot \frac11$
• $\frac{\frac ab}{\frac cd} = \frac{ad}{bc}$

I assume you already know these properties. Then, you have

$$\frac{1}{n\cdot \frac{1}{150}} = \frac{1\cdot \frac11}{n\cdot \frac{1}{150}} = \frac{1}{n}\cdot\frac{\frac11}{\frac1{150}}=\frac{1}{n}\cdot\left(\frac{150\cdot 1}{1\cdot 1}\right)=\frac{1}{n}\cdot 150$$