College

[tex]\[ \frac{6}{7} \div \frac{7}{10} = ? \][/tex]

A. [tex]\(\frac{60}{49}\)[/tex]
B. [tex]\(\frac{30}{7}\)[/tex]
C. [tex]\(\frac{49}{60}\)[/tex]
D. [tex]\(\frac{3}{5}\)[/tex]

Answer :

To solve the problem [tex]\(\frac{6}{7} \div \frac{7}{10}\)[/tex], we need to remember that dividing by a fraction is the same as multiplying by its reciprocal. Here's how we can find the answer step-by-step:

1. Identify the Problem:
We have [tex]\(\frac{6}{7} \div \frac{7}{10}\)[/tex].

2. Find the Reciprocal:
The reciprocal of [tex]\(\frac{7}{10}\)[/tex] is [tex]\(\frac{10}{7}\)[/tex].

3. Multiply by the Reciprocal:
So, [tex]\(\frac{6}{7} \div \frac{7}{10}\)[/tex] is the same as [tex]\(\frac{6}{7} \times \frac{10}{7}\)[/tex].

4. Perform the Multiplication:
Multiply the numerators: [tex]\(6 \times 10 = 60\)[/tex].

Multiply the denominators: [tex]\(7 \times 7 = 49\)[/tex].

5. Write the Result as a Fraction:
The result of the multiplication is [tex]\(\frac{60}{49}\)[/tex].

Therefore, the answer is [tex]\(\frac{60}{49}\)[/tex]. Checking it against the multiple-choice options, the correct answer is option A: [tex]\(\frac{60}{49}\)[/tex].