Solve (2/1-1/2)+(-3/4+5/1-frac{2}{5}+frac{3}{2})

$$( \frac { 2 } { 1 } - \frac { 1 } { 2 } ) + ( - \frac { 3 } { 4 } + \frac { 5 } { 1 } - \frac { 2 } { 5 } + \frac { 3 } { 2 } )$$

Evaluate

$$\frac{137}{20}=6.85$$

Solution Steps

Anything divided by one gives itself.

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

Convert 2 to fraction \frac{4}{2}.

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

Since \frac{4}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 4 to get 3.

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

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{6}{4}-\frac{3}{4}+\frac{5}{1}-\frac{2}{5}+\frac{3}{2}$$

Since \frac{6}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-3}{4}+\frac{5}{1}-\frac{2}{5}+\frac{3}{2}$$

Subtract 3 from 6 to get 3.

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

Anything divided by one gives itself.

$$\frac{3}{4}+5-\frac{2}{5}+\frac{3}{2}$$

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

$$\frac{3}{4}+\frac{20}{4}-\frac{2}{5}+\frac{3}{2}$$

Since \frac{3}{4} and \frac{20}{4} have the same denominator, add them by adding their numerators.

$$\frac{3+20}{4}-\frac{2}{5}+\frac{3}{2}$$

Add 3 and 20 to get 23.

$$\frac{23}{4}-\frac{2}{5}+\frac{3}{2}$$

Least common multiple of 4 and 5 is 20. Convert \frac{23}{4} and \frac{2}{5} to fractions with denominator 20.

$$\frac{115}{20}-\frac{8}{20}+\frac{3}{2}$$

Since \frac{115}{20} and \frac{8}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{115-8}{20}+\frac{3}{2}$$

Subtract 8 from 115 to get 107.

$$\frac{107}{20}+\frac{3}{2}$$

Least common multiple of 20 and 2 is 20. Convert \frac{107}{20} and \frac{3}{2} to fractions with denominator 20.

$$\frac{107}{20}+\frac{30}{20}$$

Since \frac{107}{20} and \frac{30}{20} have the same denominator, add them by adding their numerators.

$$\frac{107+30}{20}$$

Add 107 and 30 to get 137.

$$\frac{137}{20}$$

Factor

$$\frac{137}{2 ^ {2} \cdot 5} = 6\frac{17}{20} = 6.85$$