I really like your explanations.
As you mentioned in another post. We just need to see that in denominator we are adding something to 1, which makes the denominator greater than 1 and the overall fraction less than 1.
Hence, B>A.
Carcass wrote:
\(x= \frac{1}{1+\frac{1}{1+\frac{1}{2}}}\)
Quantity A |
Quantity B |
x |
1 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Key concept: 1/(a/b) = b/aSo, \(x= \frac{1}{1+\frac{1}{1+\frac{1}{2}}}\)
\(= \frac{1}{1+\frac{1}{\frac{2}{2}+\frac{1}{2}}}\)
\(= \frac{1}{1+\frac{1}{\frac{3}{2}}}\)
\(= \frac{1}{1+\frac{2}{3}}\)
\(= \frac{1}{\frac{3}{3}+\frac{2}{3}}\)
\(= \frac{1}{\frac{5}{3}}\)
\(= \frac{3}{5}\)
We get:
QUANTITY A: \(= \frac{3}{5}\)
QUANTITY B: \(1\)
Answer: B
Cheers,
Brent