Divide, if possible.

five sevenths
divided byStartFraction 2 Over 35 EndFraction
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Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
five sevenths
divided byStartFraction 2 Over 35 EndFraction
equals
  
enter your response here
​(Simplify your answer. Type a whole​ number, fraction, or mixed​ number.)
B.

1 answer

To divide the fraction \(\frac{5}{7}\) by the fraction \(\frac{2}{35}\), we can multiply by the reciprocal of the second fraction. Here are the steps:

  1. Write the division as multiplication by the reciprocal: \[ \frac{5}{7} \div \frac{2}{35} = \frac{5}{7} \times \frac{35}{2} \]

  2. Multiply the numerators and the denominators: \[ = \frac{5 \times 35}{7 \times 2} = \frac{175}{14} \]

  3. Simplify the fraction. We can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 7: \[ \frac{175 \div 7}{14 \div 7} = \frac{25}{2} \]

Thus, the result is: \[ \frac{5}{7} \div \frac{2}{35} = \frac{25}{2} \]

Answer:

A. five sevenths divided by StartFraction 2 Over 35 EndFraction equals \(\frac{25}{2}\) (which can also be expressed as 12.5 or \(12 \frac{1}{2}\) if desired).