Simplify 1 + 11 + 12 + 13.

Simplification & Approximation · Question 33 of 71

Question 33

MediumOriginal question

Simplify $1 + \cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{3}}}$ .

\frac{17}{10}

Correct answerYour answer

\frac{10}{7}

Correct answerYour answer

\frac{7}{3}

Correct answerYour answer

\frac{17}{7}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Start at the bottom: $2 + \frac{1}{3} = \frac{7}{3}$ , so $\frac{1}{7/3} = \frac{3}{7}$ .
Next level: $1 + \frac{3}{7} = \frac{10}{7}$ , so $\frac{1}{10/7} = \frac{7}{10}$ .
Top: $1 + \frac{7}{10} = \frac{17}{10}$ .

Worth noting

$\frac{10}{7}$ is only the middle level; forgetting to take its reciprocal gives $1 + \frac{10}{7} = \frac{17}{7}$ .

Ten questions from Simplification & Approximation, at your own pace.

Ten questions from Simplification & Approximation, at your own pace.