Question

$$ 2 \frac{1}{5} \div \frac{4}{5} $$

Short answer

The result of the division \(2 \frac{1}{5} \div \frac{4}{5}\) is \(2 \frac{3}{4}\).

Step-by-step solution

Convert the mixed number to an improper fraction

First, convert the mixed number \(2 \frac{1}{5}\) into an improper fraction. This is done by multiplying the denominator of the fraction by the whole number, then adding the numerator. The result is your new numerator. The denominator remains the same. So, \(2 \frac{1}{5}\) becomes \(\frac{11}{5}\).

Apply the 'Keep, Change, Flip' method

Next, apply the 'Keep, Change, Flip' method. So, the division problem \(2 \frac{1}{5} \div \frac{4}{5}\) becomes \(\frac{11}{5} * \frac{5}{4}\).

Multiply the fractions

Multiply the two fractions together, multiplying the nominators with each other and the denominators with each other. This gives \(\frac{55}{20}\).

Simplify the fraction

Finally, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). The simplified fraction is \(\frac{11}{4}\), or the mixed number \(2 \frac{3}{4}\).