Solve 4/5*13/4/8frac{5{7}+43/5+2}=

$$\frac { \frac { 4 } { 5 } \times 1 \frac { 3 } { 4 } } { 8 \frac { 5 } { 7 } + 4 \frac { 3 } { 5 } + 2 } =$$

Evaluate

$$\frac{49}{536}\approx 0.09141791$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{\frac{4}{5}\times \frac{4+3}{4}}{\frac{8\times 7+5}{7}+\frac{4\times 5+3}{5}+2}$$

Add 4 and 3 to get 7.

$$\frac{\frac{4}{5}\times \frac{7}{4}}{\frac{8\times 7+5}{7}+\frac{4\times 5+3}{5}+2}$$

Multiply \frac{4}{5} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4\times 7}{5\times 4}}{\frac{8\times 7+5}{7}+\frac{4\times 5+3}{5}+2}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{7}{5}}{\frac{8\times 7+5}{7}+\frac{4\times 5+3}{5}+2}$$

Multiply 8 and 7 to get 56.

$$\frac{\frac{7}{5}}{\frac{56+5}{7}+\frac{4\times 5+3}{5}+2}$$

Add 56 and 5 to get 61.

$$\frac{\frac{7}{5}}{\frac{61}{7}+\frac{4\times 5+3}{5}+2}$$

Multiply 4 and 5 to get 20.

$$\frac{\frac{7}{5}}{\frac{61}{7}+\frac{20+3}{5}+2}$$

Add 20 and 3 to get 23.

$$\frac{\frac{7}{5}}{\frac{61}{7}+\frac{23}{5}+2}$$

Least common multiple of 7 and 5 is 35. Convert \frac{61}{7} and \frac{23}{5} to fractions with denominator 35.

$$\frac{\frac{7}{5}}{\frac{305}{35}+\frac{161}{35}+2}$$

Since \frac{305}{35} and \frac{161}{35} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{5}}{\frac{305+161}{35}+2}$$

Add 305 and 161 to get 466.

$$\frac{\frac{7}{5}}{\frac{466}{35}+2}$$

Convert 2 to fraction \frac{70}{35}.

$$\frac{\frac{7}{5}}{\frac{466}{35}+\frac{70}{35}}$$

Since \frac{466}{35} and \frac{70}{35} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{5}}{\frac{466+70}{35}}$$

Add 466 and 70 to get 536.

$$\frac{\frac{7}{5}}{\frac{536}{35}}$$

Divide \frac{7}{5} by \frac{536}{35} by multiplying \frac{7}{5} by the reciprocal of \frac{536}{35}.

$$\frac{7}{5}\times \frac{35}{536}$$

Multiply \frac{7}{5} times \frac{35}{536} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 35}{5\times 536}$$

Do the multiplications in the fraction \frac{7\times 35}{5\times 536}.

$$\frac{245}{2680}$$

Reduce the fraction \frac{245}{2680} to lowest terms by extracting and canceling out 5.

$$\frac{49}{536}$$

Factor

$$\frac{7 ^ {2}}{2 ^ {3} \cdot 67} = 0.0914179104477612$$