Solve m:2/5-1/2+1/5-5/2=

$$m : \frac { 2 } { 5 } - \frac { 1 } { 2 } + \frac { 1 } { 5 } - \frac { 5 } { 2 } =$$

Evaluate

$$\frac{5m}{2}-\frac{14}{5}$$

Short Solution Steps

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

$$\frac{m\times 5}{2}-\frac{1}{2}+\frac{1}{5}-\frac{5}{2}$$

Least common multiple of 2 and 5 is 10. Convert -\frac{1}{2} and \frac{1}{5} to fractions with denominator 10.

$$\frac{m\times 5}{2}-\frac{5}{10}+\frac{2}{10}-\frac{5}{2}$$

Since -\frac{5}{10} and \frac{2}{10} have the same denominator, add them by adding their numerators.

$$\frac{m\times 5}{2}+\frac{-5+2}{10}-\frac{5}{2}$$

Add -5 and 2 to get -3.

$$\frac{m\times 5}{2}-\frac{3}{10}-\frac{5}{2}$$

Least common multiple of 10 and 2 is 10. Convert -\frac{3}{10} and \frac{5}{2} to fractions with denominator 10.

$$\frac{m\times 5}{2}-\frac{3}{10}-\frac{25}{10}$$

Since -\frac{3}{10} and \frac{25}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{m\times 5}{2}+\frac{-3-25}{10}$$

Subtract 25 from -3 to get -28.

$$\frac{m\times 5}{2}+\frac{-28}{10}$$

Reduce the fraction \frac{-28}{10} to lowest terms by extracting and canceling out 2.

$$\frac{m\times 5}{2}-\frac{14}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 5 is 10. Multiply \frac{m\times 5}{2} times \frac{5}{5}. Multiply \frac{14}{5} times \frac{2}{2}.

$$\frac{5m\times 5}{10}-\frac{14\times 2}{10}$$

Since \frac{5m\times 5}{10} and \frac{14\times 2}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5m\times 5-14\times 2}{10}$$

Do the multiplications in 5m\times 5-14\times 2.

$$\frac{25m-28}{10}$$

Factor

$$\frac{25m-28}{10}$$

Solution Steps

Factor out \frac{1}{10}.

$$\frac{25m-28}{10}$$

Consider 25m-5+2-25. Multiply and combine like terms.

$$25m-28$$

Rewrite the complete factored expression.

$$\frac{25m-28}{10}$$