Solve (32/5-32/4+7)-(-1/5-7/4+2)

$$( \frac { 32 } { 5 } - \frac { 32 } { 4 } + 7 ) - ( - \frac { 1 } { 5 } - \frac { 7 } { 4 } + 2 )$$

Evaluate

$$\frac{107}{20}=5.35$$

Solution Steps

Divide 32 by 4 to get 8.

$$\frac{32}{5}-8+7-\left(-\frac{1}{5}-\frac{7}{4}+2\right)$$

Convert 8 to fraction \frac{40}{5}.

$$\frac{32}{5}-\frac{40}{5}+7-\left(-\frac{1}{5}-\frac{7}{4}+2\right)$$

Since \frac{32}{5} and \frac{40}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{32-40}{5}+7-\left(-\frac{1}{5}-\frac{7}{4}+2\right)$$

Subtract 40 from 32 to get -8.

$$-\frac{8}{5}+7-\left(-\frac{1}{5}-\frac{7}{4}+2\right)$$

Convert 7 to fraction \frac{35}{5}.

$$-\frac{8}{5}+\frac{35}{5}-\left(-\frac{1}{5}-\frac{7}{4}+2\right)$$

Since -\frac{8}{5} and \frac{35}{5} have the same denominator, add them by adding their numerators.

$$\frac{-8+35}{5}-\left(-\frac{1}{5}-\frac{7}{4}+2\right)$$

Add -8 and 35 to get 27.

$$\frac{27}{5}-\left(-\frac{1}{5}-\frac{7}{4}+2\right)$$

Least common multiple of 5 and 4 is 20. Convert -\frac{1}{5} and \frac{7}{4} to fractions with denominator 20.

$$\frac{27}{5}-\left(-\frac{4}{20}-\frac{35}{20}+2\right)$$

Since -\frac{4}{20} and \frac{35}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27}{5}-\left(\frac{-4-35}{20}+2\right)$$

Subtract 35 from -4 to get -39.

$$\frac{27}{5}-\left(-\frac{39}{20}+2\right)$$

Convert 2 to fraction \frac{40}{20}.

$$\frac{27}{5}-\left(-\frac{39}{20}+\frac{40}{20}\right)$$

Since -\frac{39}{20} and \frac{40}{20} have the same denominator, add them by adding their numerators.

$$\frac{27}{5}-\frac{-39+40}{20}$$

Add -39 and 40 to get 1.

$$\frac{27}{5}-\frac{1}{20}$$

Least common multiple of 5 and 20 is 20. Convert \frac{27}{5} and \frac{1}{20} to fractions with denominator 20.

$$\frac{108}{20}-\frac{1}{20}$$

Since \frac{108}{20} and \frac{1}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{108-1}{20}$$

Subtract 1 from 108 to get 107.

$$\frac{107}{20}$$

Factor

$$\frac{107}{2 ^ {2} \cdot 5} = 5\frac{7}{20} = 5.35$$