Solve 63/4:(7/2-3/4+1/5)=

$$6 \frac { 3 } { 4 } : ( \frac { 7 } { 2 } - \frac { 3 } { 4 } + \frac { 1 } { 5 } ) =$$

Evaluate

$$\frac{135}{59}\approx 2.288135593$$

Solution Steps

Multiply 6 and 4 to get 24.

$$\frac{\frac{24+3}{4}}{\frac{7}{2}-\frac{3}{4}+\frac{1}{5}}$$

Add 24 and 3 to get 27.

$$\frac{\frac{27}{4}}{\frac{7}{2}-\frac{3}{4}+\frac{1}{5}}$$

Least common multiple of 2 and 4 is 4. Convert \frac{7}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{\frac{27}{4}}{\frac{14}{4}-\frac{3}{4}+\frac{1}{5}}$$

Since \frac{14}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{27}{4}}{\frac{14-3}{4}+\frac{1}{5}}$$

Subtract 3 from 14 to get 11.

$$\frac{\frac{27}{4}}{\frac{11}{4}+\frac{1}{5}}$$

Least common multiple of 4 and 5 is 20. Convert \frac{11}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{\frac{27}{4}}{\frac{55}{20}+\frac{4}{20}}$$

Since \frac{55}{20} and \frac{4}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{27}{4}}{\frac{55+4}{20}}$$

Add 55 and 4 to get 59.

$$\frac{\frac{27}{4}}{\frac{59}{20}}$$

Divide \frac{27}{4} by \frac{59}{20} by multiplying \frac{27}{4} by the reciprocal of \frac{59}{20}.

$$\frac{27}{4}\times \frac{20}{59}$$

Multiply \frac{27}{4} times \frac{20}{59} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27\times 20}{4\times 59}$$

Do the multiplications in the fraction \frac{27\times 20}{4\times 59}.

$$\frac{540}{236}$$

Reduce the fraction \frac{540}{236} to lowest terms by extracting and canceling out 4.

$$\frac{135}{59}$$

Factor

$$\frac{3 ^ {3} \cdot 5}{59} = 2\frac{17}{59} = 2.288135593220339$$