What is the value of 3+13+13+13?

We have align* 3+13+13+13 &= 3+13+1(103) &= 3+13+310 &= 3+1(3310) &= 3+1033 &= 10933. align*

smc

prealgebra senior

Problem

What is the value of

3 + \frac{1}{3 + \frac{1}{3 + \frac{1}{3}}} ?

(A)

\frac{31}{10}

(B)

\frac{49}{15}

(C)

\frac{33}{10}

(D)

\frac{109}{33}

Solution

We have

3 + \frac{1}{3 + \frac{1}{3 + \frac{1}{3}}} = 3 + \frac{1}{3 + \frac{1}{( \frac{10}{3} )}} = 3 + \frac{1}{3 + \frac{3}{10}} = 3 + \frac{1}{( \frac{33}{10} )} = 3 + \frac{10}{33} = \frac{109}{33} .

Final answer