Question
Simplify the following complex fraction. 3/4 / 5/3 x 1/6
A. 5/24
B. 3/40
C. 9/20
D. 27/10
A. 5/24
B. 3/40
C. 9/20
D. 27/10
Answers
Answered by
GPT-4o mini
To simplify the complex fraction \(\frac{3/4}{5/3} \times \frac{1}{6}\), we can follow these steps:
1. First, simplify \(\frac{3/4}{5/3}\):
\[
\frac{3/4}{5/3} = \frac{3}{4} \times \frac{3}{5} = \frac{3 \times 3}{4 \times 5} = \frac{9}{20}
\]
2. Now, we multiply this result by \(\frac{1}{6}\):
\[
\frac{9}{20} \times \frac{1}{6} = \frac{9 \times 1}{20 \times 6} = \frac{9}{120}
\]
3. Finally, simplify \(\frac{9}{120}\):
The greatest common divisor (GCD) of 9 and 120 is 3. Dividing both the numerator and denominator by 3 gives us:
\[
\frac{9 \div 3}{120 \div 3} = \frac{3}{40}
\]
Thus, the simplified result is \(\frac{3}{40}\). The answer is:
**B. \(\frac{3}{40}\)**
1. First, simplify \(\frac{3/4}{5/3}\):
\[
\frac{3/4}{5/3} = \frac{3}{4} \times \frac{3}{5} = \frac{3 \times 3}{4 \times 5} = \frac{9}{20}
\]
2. Now, we multiply this result by \(\frac{1}{6}\):
\[
\frac{9}{20} \times \frac{1}{6} = \frac{9 \times 1}{20 \times 6} = \frac{9}{120}
\]
3. Finally, simplify \(\frac{9}{120}\):
The greatest common divisor (GCD) of 9 and 120 is 3. Dividing both the numerator and denominator by 3 gives us:
\[
\frac{9 \div 3}{120 \div 3} = \frac{3}{40}
\]
Thus, the simplified result is \(\frac{3}{40}\). The answer is:
**B. \(\frac{3}{40}\)**