Question

$$ \frac{6}{5} \div \frac{3}{10} $$

Short answer

The result of the division \(\frac{6}{5} \div \frac{3}{10}\) is \(4\).

Step-by-step solution

Identify the two fractions and the operation

The first fraction is \(\frac{6}{5}\) and the second fraction is \(\frac{3}{10}\). The operation to be completed is division.

Find the reciprocal of the second fraction

To find the reciprocal of a fraction, simply interchange the numerator and denominator. The reciprocal of \(\frac{3}{10}\) is \(\frac{10}{3}\).

Multiply the first fraction by the reciprocal of the second fraction

Now, instead of dividing, one is going to multiply the first fraction \(\frac{6}{5}\) by the reciprocal of the second fraction \(\frac{10}{3}\). Write it down as: \(\frac{6}{5} \times \frac{10}{3}\).

Solve the multiplication problem

To solve the multiplication problem, multiply the numerators together to get the numerator of the result, and then multiply the denominators together to get the denominator of the result. This yields: \(\frac{6 \times 10}{5 \times 3} = \frac{60}{15}\).

Simplify the resulting fraction

The fraction \(\frac{60}{15}\) simplifies to \(4\). This is done by dividing both the numerator and the denominator of the fraction by their greatest common divisor (GCD), which in this case is \(15\).