Which of the following represents the correct simplified value of the continued fraction: \(x = 1 + \cfrac{1}{2 + \cfrac{1}{2 + \tfrac{1}{2}}}\)
\(\dfrac{17}{12}\)
Work from the inside out.
Step 1 – Innermost: \(2 + \tfrac{1}{2} = \dfrac{5}{2}\)
Step 2 – Next layer: \(2 + \dfrac{1}{\,5/2\,} = 2 + \dfrac{2}{5} = \dfrac{12}{5}\)
Step 3 – Outermost: \(x = 1 + \dfrac{1}{\,12/5\,} = 1 + \dfrac{5}{12} = \dfrac{17}{12}\)
Hence \(x = \dfrac{17}{12}\).
Which of the following fractions is the largest?
2/3, 6/53, 79/90, 33/44
Add \(\dfrac{1}{8} + \dfrac{1}{16}\) and express the result as a decimal.
If 11 / 19 = A and 2 / 9 = B, then what is A - B?
A tank holds \(5\tfrac{3}{4}\) liters of water. If 2.375 liters are drained twice, how much water remains?
What is the result of \(2\tfrac{1}{4} \div 0.5\)?
Convert 3.375 into a fraction in simplest form.
Express 0.121212... as a fraction.
Evaluate the continued fraction: \(x = 2 + \dfrac{1}{3 + \dfrac{1}{4 + \tfrac{1}{2}}}\)
Which of the following fractions is the largest?
3/7 , 7/53 , 41/80 , 29/79
The value of $\frac{5}{3} + (\frac{1}{1+\frac{5}{6}}) - \frac{5}{3}$ is
The value of $\frac{4}{5} + (\frac{1}{1+\frac{5}{6}}) - \frac{2}{5}$ is