Solve 7/frac{7{8}+8/10}=

$$\frac { 7 } { \frac { 7 } { 8 } + \frac { 8 } { 10 } } =$$

Evaluate

$$\frac{280}{67}\approx 4.179104478$$

Solution Steps

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{7}{\frac{7}{8}+\frac{4}{5}}$$

Least common multiple of 8 and 5 is 40. Convert \frac{7}{8} and \frac{4}{5} to fractions with denominator 40.

$$\frac{7}{\frac{35}{40}+\frac{32}{40}}$$

Since \frac{35}{40} and \frac{32}{40} have the same denominator, add them by adding their numerators.

$$\frac{7}{\frac{35+32}{40}}$$

Add 35 and 32 to get 67.

$$\frac{7}{\frac{67}{40}}$$

Divide 7 by \frac{67}{40} by multiplying 7 by the reciprocal of \frac{67}{40}.

$$7\times \frac{40}{67}$$

Express 7\times \frac{40}{67} as a single fraction.

$$\frac{7\times 40}{67}$$

Multiply 7 and 40 to get 280.

$$\frac{280}{67}$$

Factor

$$\frac{2 ^ {3} \cdot 5 \cdot 7}{67} = 4\frac{12}{67} = 4.17910447761194$$