To find the quotient of [tex]\(\frac{3}{4} \div \frac{5}{7}\)[/tex], we need to follow these steps:
1. Understand the division of fractions:
Division of fractions can be converted into multiplication by the reciprocal. This means that dividing by a fraction is the same as multiplying by its reciprocal.
2. Find the reciprocal:
The reciprocal of [tex]\(\frac{5}{7}\)[/tex] is [tex]\(\frac{7}{5}\)[/tex].
3. Set up the multiplication:
Now, we need to multiply [tex]\(\frac{3}{4}\)[/tex] by [tex]\(\frac{7}{5}\)[/tex].
[tex]\[
\frac{3}{4} \times \frac{7}{5}
\][/tex]
4. Multiply the numerators:
The numerator of the resulting fraction is obtained by multiplying the numerators of the given fractions.
[tex]\[
3 \times 7 = 21
\][/tex]
5. Multiply the denominators:
The denominator of the resulting fraction is obtained by multiplying the denominators of the given fractions.
[tex]\[
4 \times 5 = 20
\][/tex]
6. Form the resulting fraction:
Combining the multiplied numerators and denominators, we get:
[tex]\[
\frac{21}{20}
\][/tex]
So, the quotient of [tex]\(\frac{3}{4} \div \frac{5}{7}\)[/tex] is [tex]\(\frac{21}{20}\)[/tex]. This corresponds to option D.
Therefore, the correct answer is:
[tex]\[ D. \frac{21}{20} \][/tex]
