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What is the quotient of [tex]$\frac{3}{4} \div \frac{5}{7}$[/tex]?

A. [tex]$\frac{15}{28}$[/tex]

B. [tex][tex]$\frac{20}{21}$[/tex][/tex]

C. [tex]$\frac{28}{15}$[/tex]

D. [tex]$\frac{21}{20}$[/tex]

Sagot :

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]
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