To divide the fractions [tex]\( \frac{7}{24} \)[/tex] by [tex]\( \frac{35}{48} \)[/tex], we follow these steps:
1. Invert the second fraction (reciprocal):
[tex]\[
\frac{35}{48} \text{ becomes } \frac{48}{35}
\][/tex]
2. Multiply the first fraction by the reciprocal of the second fraction:
[tex]\[
\frac{7}{24} \times \frac{48}{35}
\][/tex]
3. Multiply the numerators together and the denominators together:
[tex]\[
\frac{7 \times 48}{24 \times 35} = \frac{336}{840}
\][/tex]
4. Reduce the fraction [tex]\( \frac{336}{840} \)[/tex] to its lowest terms:
- Find the greatest common divisor (GCD) of 336 and 840. The GCD is 168.
- Divide both the numerator and the denominator by the GCD:
[tex]\[
\frac{336 \div 168}{840 \div 168} = \frac{2}{5}
\][/tex]
Therefore, the quotient reduced to its lowest terms is [tex]\( \frac{2}{5} \)[/tex].
So, the best answer is:
A. [tex]\( \frac{2}{5} \)[/tex]
