Answer :

We want to evaluate

[tex]$$
\frac{14}{15} \div \frac{10}{21}.
$$[/tex]

Step 1. Rewrite the division as a multiplication:
Dividing by a fraction is the same as multiplying by its reciprocal. So,

[tex]$$
\frac{14}{15} \div \frac{10}{21} = \frac{14}{15} \times \frac{21}{10}.
$$[/tex]

Step 2. Multiply the fractions:
Multiply the numerators together and the denominators together:

[tex]$$
\frac{14 \times 21}{15 \times 10} = \frac{294}{150}.
$$[/tex]

Step 3. Simplify the fraction:
To simplify [tex]$\frac{294}{150}$[/tex], we divide both the numerator and the denominator by their greatest common divisor. In this case, the greatest common divisor is [tex]$6$[/tex], so

[tex]$$
\frac{294}{150} = \frac{294 \div 6}{150 \div 6} = \frac{49}{25}.
$$[/tex]

Thus, the final answer is

[tex]$$
\frac{49}{25}.
$$[/tex]

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Rewritten by : Barada