To solve the problem of dividing [tex]\(\frac{7}{8}\)[/tex] by [tex]\(\frac{3}{8}\)[/tex], we follow these steps:
1. Understand Division of Fractions:
To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator.
2. Write Down the Problem:
[tex]\[
\frac{7}{8} \div \frac{3}{8}
\][/tex]
3. Find the Reciprocal of the Second Fraction:
The reciprocal of [tex]\(\frac{3}{8}\)[/tex] is [tex]\(\frac{8}{3}\)[/tex].
4. Replace Division with Multiplication by the Reciprocal:
Now, we need to find:
[tex]\[
\frac{7}{8} \times \frac{8}{3}
\][/tex]
5. Multiply the Numerators Together:
[tex]\[
7 \times 8 = 56
\][/tex]
6. Multiply the Denominators Together:
[tex]\[
8 \times 3 = 24
\][/tex]
7. Form the New Fraction:
The product of the numerators over the product of the denominators gives us:
[tex]\[
\frac{56}{24}
\][/tex]
8. Simplify if Necessary:
To simplify [tex]\(\frac{56}{24}\)[/tex], divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 56 and 24 is 8.
[tex]\[
\frac{56 \div 8}{24 \div 8} = \frac{7}{3}
\][/tex]
9. Convert the Improper Fraction to a Mixed Number:
[tex]\[
\frac{7}{3} = 2 \frac{1}{3}
\][/tex]
Thus, the quotient of [tex]\(\frac{7}{8} \div \frac{3}{8}\)[/tex] is:
[tex]\[
2 \frac{1}{3}
\][/tex]
Hence, the correct answer from the given options is:
[tex]\[
2 \frac{1}{3}
\][/tex]
