Question

If $\frac{16}{23} = \frac{1}{a + \frac{1}{b + \frac{1}{c + \frac{1}{2} } } }$ then which one is right?
A) a + b = c
B) a – c = b
C) a + c = b
D) a × c = b

Answer 1

Answer:

A) a + b = c

Step-by-step explanation:

$\displaystyle\frac{16}{23}=\frac{1}{\frac{23}{16}}\\\\=\frac1{1+\frac7{16}}\\\\\\=\frac1{1+\dfrac1{\frac{16}7}}\\\\\\=\frac1{1+\dfrac1{2+\frac27}}\\\\\\=\frac1{1+\dfrac1{2+\dfrac1{\frac72}}}\\\\\\=\frac1{1+\dfrac1{2+\dfrac1{3+\frac12}}}$

So a = 1, b = 2, c = 3.

Thus a + b = c.