Solve 7-3/2+1/10/frac{frac{2{5}-1}{2}+1/5}

$$\frac { 7 - \frac { 3 } { 2 } + \frac { 1 } { 10 } } { \frac { \frac { 2 } { 5 } - 1 } { 2 } + \frac { 1 } { 5 } }$$

Evaluate

$$-56$$

Solution Steps

Convert 7 to fraction \frac{14}{2}.

$$\frac{\frac{14}{2}-\frac{3}{2}+\frac{1}{10}}{\frac{\frac{2}{5}-1}{2}+\frac{1}{5}}$$

Since \frac{14}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{14-3}{2}+\frac{1}{10}}{\frac{\frac{2}{5}-1}{2}+\frac{1}{5}}$$

Subtract 3 from 14 to get 11.

$$\frac{\frac{11}{2}+\frac{1}{10}}{\frac{\frac{2}{5}-1}{2}+\frac{1}{5}}$$

Least common multiple of 2 and 10 is 10. Convert \frac{11}{2} and \frac{1}{10} to fractions with denominator 10.

$$\frac{\frac{55}{10}+\frac{1}{10}}{\frac{\frac{2}{5}-1}{2}+\frac{1}{5}}$$

Since \frac{55}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{55+1}{10}}{\frac{\frac{2}{5}-1}{2}+\frac{1}{5}}$$

Add 55 and 1 to get 56.

$$\frac{\frac{56}{10}}{\frac{\frac{2}{5}-1}{2}+\frac{1}{5}}$$

Reduce the fraction \frac{56}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{28}{5}}{\frac{\frac{2}{5}-1}{2}+\frac{1}{5}}$$

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

$$\frac{\frac{28}{5}}{\frac{\frac{2}{5}-\frac{5}{5}}{2}+\frac{1}{5}}$$

Since \frac{2}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{28}{5}}{\frac{\frac{2-5}{5}}{2}+\frac{1}{5}}$$

Subtract 5 from 2 to get -3.

$$\frac{\frac{28}{5}}{\frac{-\frac{3}{5}}{2}+\frac{1}{5}}$$

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

$$\frac{\frac{28}{5}}{\frac{-3}{5\times 2}+\frac{1}{5}}$$

Multiply 5 and 2 to get 10.

$$\frac{\frac{28}{5}}{\frac{-3}{10}+\frac{1}{5}}$$

Fraction \frac{-3}{10} can be rewritten as -\frac{3}{10} by extracting the negative sign.

$$\frac{\frac{28}{5}}{-\frac{3}{10}+\frac{1}{5}}$$

Least common multiple of 10 and 5 is 10. Convert -\frac{3}{10} and \frac{1}{5} to fractions with denominator 10.

$$\frac{\frac{28}{5}}{-\frac{3}{10}+\frac{2}{10}}$$

Since -\frac{3}{10} and \frac{2}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{28}{5}}{\frac{-3+2}{10}}$$

Add -3 and 2 to get -1.

$$\frac{\frac{28}{5}}{-\frac{1}{10}}$$

Divide \frac{28}{5} by -\frac{1}{10} by multiplying \frac{28}{5} by the reciprocal of -\frac{1}{10}.

$$\frac{28}{5}\left(-10\right)$$

Express \frac{28}{5}\left(-10\right) as a single fraction.

$$\frac{28\left(-10\right)}{5}$$

Multiply 28 and -10 to get -280.

$$\frac{-280}{5}$$

Divide -280 by 5 to get -56.

$$-56$$

Factor

$$-56$$