Solve n/frac{2{5}}-1/2+1/5-3/2=

$$\frac{ n }{ \frac{ 2 }{ 5 } } - \frac{ 1 }{ 2 } + \frac{ 1 }{ 5 } - \frac{ 3 }{ 2 } =$$

Evaluate

$$\frac{5n}{2}-\frac{9}{5}$$

Short Solution Steps

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

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

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

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

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

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

Add -5 and 2 to get -3.

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

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

$$\frac{n\times 5}{2}-\frac{3}{10}-\frac{15}{10}$$

Since -\frac{3}{10} and \frac{15}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{n\times 5}{2}+\frac{-3-15}{10}$$

Subtract 15 from -3 to get -18.

$$\frac{n\times 5}{2}+\frac{-18}{10}$$

Reduce the fraction \frac{-18}{10} to lowest terms by extracting and canceling out 2.

$$\frac{n\times 5}{2}-\frac{9}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 5 is 10. Multiply \frac{n\times 5}{2} times \frac{5}{5}. Multiply \frac{9}{5} times \frac{2}{2}.

$$\frac{5n\times 5}{10}-\frac{9\times 2}{10}$$

Since \frac{5n\times 5}{10} and \frac{9\times 2}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5n\times 5-9\times 2}{10}$$

Do the multiplications in 5n\times 5-9\times 2.

$$\frac{25n-18}{10}$$

Factor

$$\frac{25n-18}{10}$$

Solution Steps

Factor out \frac{1}{10}.

$$\frac{25n-18}{10}$$

Consider 25n-5+2-15. Multiply and combine like terms.

$$25n-18$$

Rewrite the complete factored expression.

$$\frac{25n-18}{10}$$