Solve 5.2/4-frac{4{5}}

$$\frac { 5.2 } { 4 - \frac { 4 } { 5 } }$$

Evaluate

$$1.625$$

Solution Steps

Convert 4 to fraction \frac{20}{5}.

$$\frac{5.2}{\frac{20}{5}-\frac{4}{5}}$$

Since \frac{20}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5.2}{\frac{20-4}{5}}$$

Subtract 4 from 20 to get 16.

$$\frac{5.2}{\frac{16}{5}}$$

Divide 5.2 by \frac{16}{5} by multiplying 5.2 by the reciprocal of \frac{16}{5}.

$$5.2\times \frac{5}{16}$$

Convert decimal number 5.2 to fraction \frac{52}{10}. Reduce the fraction \frac{52}{10} to lowest terms by extracting and canceling out 2.

$$\frac{26}{5}\times \frac{5}{16}$$

Multiply \frac{26}{5} times \frac{5}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{26\times 5}{5\times 16}$$

Cancel out 5 in both numerator and denominator.

$$\frac{26}{16}$$

Reduce the fraction \frac{26}{16} to lowest terms by extracting and canceling out 2.

$$\frac{13}{8}$$

Factor

$$\frac{13}{2 ^ {3}} = 1\frac{5}{8} = 1.625$$