To solve the problem of dividing [tex]\( \frac{7}{24} \)[/tex] by [tex]\( \frac{35}{48} \)[/tex] and reducing the quotient to its lowest terms, let's go through the steps one by one.
1. Rewrite the division of fractions as multiplication by the reciprocal:
[tex]\[\frac{7}{24} \div \frac{35}{48} = \frac{7}{24} \times \frac{48}{35}\][/tex]
2. Multiply the numerators together and the denominators together:
[tex]\[\left(\frac{7}{24} \times \frac{48}{35}\right) = \frac{7 \times 48}{24 \times 35} = \frac{336}{840}\][/tex]
So the quotient before reduction is [tex]\(\frac{336}{840}\)[/tex].
3. Find the Greatest Common Divisor (GCD) of the numerator and the denominator to reduce the fraction:
The GCD of 336 and 840 is 168.
4. Divide both the numerator and the denominator by their GCD:
[tex]\[\frac{336 \div 168}{840 \div 168} = \frac{2}{5}\][/tex]
So, the quotient reduced to its lowest terms is [tex]\( \frac{2}{5} \)[/tex].
Therefore, the best answer for the given question is:
D. [tex]\( \frac{2}{5} \)[/tex]
