Solve 3/frac{5{2}}-7/5-2/1-frac{4{5}}

$$\frac { 3 } { \frac { 5 } { 2 } } - \frac { \frac { 7 } { 5 } - 2 } { 1 - \frac { 4 } { 5 } }$$

Evaluate

$$\frac{21}{5}=4.2$$

Solution Steps

Divide 3 by \frac{5}{2} by multiplying 3 by the reciprocal of \frac{5}{2}.

$$3\times \frac{2}{5}-\frac{\frac{7}{5}-2}{1-\frac{4}{5}}$$

Express 3\times \frac{2}{5} as a single fraction.

$$\frac{3\times 2}{5}-\frac{\frac{7}{5}-2}{1-\frac{4}{5}}$$

Multiply 3 and 2 to get 6.

$$\frac{6}{5}-\frac{\frac{7}{5}-2}{1-\frac{4}{5}}$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{6}{5}-\frac{\frac{7}{5}-\frac{10}{5}}{1-\frac{4}{5}}$$

Since \frac{7}{5} and \frac{10}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6}{5}-\frac{\frac{7-10}{5}}{1-\frac{4}{5}}$$

Subtract 10 from 7 to get -3.

$$\frac{6}{5}-\frac{-\frac{3}{5}}{1-\frac{4}{5}}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{6}{5}-\frac{-\frac{3}{5}}{\frac{5}{5}-\frac{4}{5}}$$

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

$$\frac{6}{5}-\frac{-\frac{3}{5}}{\frac{5-4}{5}}$$

Subtract 4 from 5 to get 1.

$$\frac{6}{5}-\frac{-\frac{3}{5}}{\frac{1}{5}}$$

Divide -\frac{3}{5} by \frac{1}{5} by multiplying -\frac{3}{5} by the reciprocal of \frac{1}{5}.

$$\frac{6}{5}-\left(-\frac{3}{5}\times 5\right)$$

Cancel out 5 and 5.

$$\frac{6}{5}-\left(-3\right)$$

The opposite of -3 is 3.

$$\frac{6}{5}+3$$

Convert 3 to fraction \frac{15}{5}.

$$\frac{6}{5}+\frac{15}{5}$$

Since \frac{6}{5} and \frac{15}{5} have the same denominator, add them by adding their numerators.

$$\frac{6+15}{5}$$

Add 6 and 15 to get 21.

$$\frac{21}{5}$$

Factor

$$\frac{3 \cdot 7}{5} = 4\frac{1}{5} = 4.2$$