To divide the fraction [tex]\(\frac{7}{24}\)[/tex] by the fraction [tex]\(\frac{35}{48}\)[/tex], we will use the rule for dividing fractions: [tex]\(\left(\frac{a}{b}\right) \div \left(\frac{c}{d}\right) = \left(\frac{a}{b}\right) \times \left(\frac{d}{c}\right)\)[/tex]. This means flipping the second fraction and then multiplying.
Let's go through this step-by-step:
1. Rewrite the division as a multiplication problem:
[tex]\[
\frac{7}{24} \div \frac{35}{48} = \frac{7}{24} \times \frac{48}{35}
\][/tex]
2. Multiply the numerators and the denominators:
[tex]\[
\frac{7 \times 48}{24 \times 35}
\][/tex]
3. Perform the multiplications in the numerator and the denominator:
[tex]\[
7 \times 48 = 336
\][/tex]
[tex]\[
24 \times 35 = 840
\][/tex]
So, we now have:
[tex]\[
\frac{336}{840}
\][/tex]
4. Reduce the fraction to its lowest terms.
To do this, find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 336 and 840 is 168.
Now, divide both the numerator and the denominator by the GCD:
[tex]\[
\frac{336 \div 168}{840 \div 168} = \frac{2}{5}
\][/tex]
Thus, 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]
So, the correct answer is:
[tex]\(C. \frac{2}{5}\)[/tex]
