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, follow these steps:
1. Recall how to divide fractions: To divide by a fraction, multiply by its reciprocal. This means that [tex]\(\frac{7}{24} \div \frac{35}{48}\)[/tex] is equivalent to [tex]\(\frac{7}{24} \times \frac{48}{35}\)[/tex].
2. Multiply the fractions:
[tex]\[
\frac{7}{24} \times \frac{48}{35}
\][/tex]
3. Simplify the multiplication:
- Multiply the numerators: [tex]\(7 \times 48 = 336\)[/tex]
- Multiply the denominators: [tex]\(24 \times 35 = 840\)[/tex]
So, [tex]\(\frac{7}{24} \times \frac{48}{35} = \frac{336}{840}\)[/tex].
4. Reduce the fraction: To reduce [tex]\(\frac{336}{840}\)[/tex] to its lowest terms, find the greatest common divisor (GCD) of 336 and 840. The GCD of 336 and 840 is 168.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{336 \div 168}{840 \div 168} = \frac{2}{5}
\][/tex]
So, the reduced fraction is [tex]\(\frac{2}{5}\)[/tex].
Therefore, the best answer is:
D. [tex]\(\frac{2}{5}\)[/tex]
