Solve 35/14:5/27+5:35/14-27/5:3=

$$\frac { 35 } { 14 } : \frac { 5 } { 27 } + 5 : \frac { 35 } { 14 } - \frac { 27 } { 5 } : 3 =$$

Evaluate

$$\frac{137}{10}=13.7$$

Solution Steps

Divide \frac{35}{14} by \frac{5}{27} by multiplying \frac{35}{14} by the reciprocal of \frac{5}{27}.

$$\frac{35\times 27}{14\times 5}+\frac{5}{\frac{35}{14}}-\frac{\frac{27}{5}}{3}$$

Cancel out 5\times 7 in both numerator and denominator.

$$\frac{27}{2}+\frac{5}{\frac{35}{14}}-\frac{\frac{27}{5}}{3}$$

Divide 5 by \frac{35}{14} by multiplying 5 by the reciprocal of \frac{35}{14}.

$$\frac{27}{2}+\frac{5\times 14}{35}-\frac{\frac{27}{5}}{3}$$

Multiply 5 and 14 to get 70.

$$\frac{27}{2}+\frac{70}{35}-\frac{\frac{27}{5}}{3}$$

Divide 70 by 35 to get 2.

$$\frac{27}{2}+2-\frac{\frac{27}{5}}{3}$$

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

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

Since \frac{27}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

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

Add 27 and 4 to get 31.

$$\frac{31}{2}-\frac{\frac{27}{5}}{3}$$

Express \frac{\frac{27}{5}}{3} as a single fraction.

$$\frac{31}{2}-\frac{27}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$\frac{31}{2}-\frac{27}{15}$$

Reduce the fraction \frac{27}{15} to lowest terms by extracting and canceling out 3.

$$\frac{31}{2}-\frac{9}{5}$$

Least common multiple of 2 and 5 is 10. Convert \frac{31}{2} and \frac{9}{5} to fractions with denominator 10.

$$\frac{155}{10}-\frac{18}{10}$$

Since \frac{155}{10} and \frac{18}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{155-18}{10}$$

Subtract 18 from 155 to get 137.

$$\frac{137}{10}$$

Factor

$$\frac{137}{2 \cdot 5} = 13\frac{7}{10} = 13.7$$