Question

What is the quotient in simplest form?

StartFraction 12 Over 7 EndFraction
StartFraction 7 Over 36 EndFraction
StartFraction 4 Over 7 EndFraction
1 and three-fourths
5 and StartFraction 1 Over 7 EndFraction

Answer 1

To find the quotient of the fractions \(\frac{12}{7}\) and \(\frac{7}{36}\), we can divide \( \frac{12}{7} \) by \( \frac{7}{36} \). Dividing by a fraction is the same as multiplying by its reciprocal.

So, we have:

\[
\frac{12}{7} \div \frac{7}{36} = \frac{12}{7} \times \frac{36}{7}
\]

Now we can perform the multiplication:

\[
\frac{12 \times 36}{7 \times 7} = \frac{432}{49}
\]

Next, we check if \(\frac{432}{49}\) can be simplified. Since \(432\) and \(49\) have no common factors (as \(49\) is \(7^2\) and \(432\) does not share any factors with \(7\)), the fraction is already in simplest form.

Thus, the quotient in simplest form is:

\[
\frac{432}{49}
\]