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. Understand the Division of Fractions:
When you divide by a fraction, you multiply by its reciprocal. Therefore, dividing [tex]\(\frac{7}{24}\)[/tex] by [tex]\(\frac{35}{48}\)[/tex] is the same as multiplying [tex]\(\frac{7}{24}\)[/tex] by [tex]\(\frac{48}{35}\)[/tex].
2. Set Up the Multiplication:
[tex]\[
\frac{7}{24} \div \frac{35}{48} = \frac{7}{24} \times \frac{48}{35}
\][/tex]
3. Multiply the Numerators and the Denominators:
[tex]\[
\frac{7 \times 48}{24 \times 35} = \frac{336}{840}
\][/tex]
4. Simplify the Fraction by Finding the Greatest Common Divisor (GCD):
The GCD of 336 and 840 is found to be 168.
Now, 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 of [tex]\(\frac{7}{24}\)[/tex] divided by [tex]\(\frac{35}{48}\)[/tex] reduced to its lowest terms is [tex]\(\frac{2}{5}\)[/tex].
Therefore, the best answer for the question is:
C. [tex]\(\frac{2}{5}\)[/tex]
