Solve (7/6+35/9*13/16)div17/4

$$( \frac { 7 } { 6 } + 3 \frac { 5 } { 9 } \times 1 \frac { 3 } { 16 } ) \div 1 \frac { 7 } { 4 }$$

Evaluate

$$\frac{194}{99}\approx 1.95959596$$

Solution Steps

Multiply 3 and 9 to get 27.

$$\frac{\frac{7}{6}+\frac{27+5}{9}\times \frac{1\times 16+3}{16}}{\frac{1\times 4+7}{4}}$$

Add 27 and 5 to get 32.

$$\frac{\frac{7}{6}+\frac{32}{9}\times \frac{1\times 16+3}{16}}{\frac{1\times 4+7}{4}}$$

Multiply 1 and 16 to get 16.

$$\frac{\frac{7}{6}+\frac{32}{9}\times \frac{16+3}{16}}{\frac{1\times 4+7}{4}}$$

Add 16 and 3 to get 19.

$$\frac{\frac{7}{6}+\frac{32}{9}\times \frac{19}{16}}{\frac{1\times 4+7}{4}}$$

Multiply \frac{32}{9} times \frac{19}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7}{6}+\frac{32\times 19}{9\times 16}}{\frac{1\times 4+7}{4}}$$

Do the multiplications in the fraction \frac{32\times 19}{9\times 16}.

$$\frac{\frac{7}{6}+\frac{608}{144}}{\frac{1\times 4+7}{4}}$$

Reduce the fraction \frac{608}{144} to lowest terms by extracting and canceling out 16.

$$\frac{\frac{7}{6}+\frac{38}{9}}{\frac{1\times 4+7}{4}}$$

Least common multiple of 6 and 9 is 18. Convert \frac{7}{6} and \frac{38}{9} to fractions with denominator 18.

$$\frac{\frac{21}{18}+\frac{76}{18}}{\frac{1\times 4+7}{4}}$$

Since \frac{21}{18} and \frac{76}{18} have the same denominator, add them by adding their numerators.

$$\frac{\frac{21+76}{18}}{\frac{1\times 4+7}{4}}$$

Add 21 and 76 to get 97.

$$\frac{\frac{97}{18}}{\frac{1\times 4+7}{4}}$$

Multiply 1 and 4 to get 4.

$$\frac{\frac{97}{18}}{\frac{4+7}{4}}$$

Add 4 and 7 to get 11.

$$\frac{\frac{97}{18}}{\frac{11}{4}}$$

Divide \frac{97}{18} by \frac{11}{4} by multiplying \frac{97}{18} by the reciprocal of \frac{11}{4}.

$$\frac{97}{18}\times \frac{4}{11}$$

Multiply \frac{97}{18} times \frac{4}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{97\times 4}{18\times 11}$$

Do the multiplications in the fraction \frac{97\times 4}{18\times 11}.

$$\frac{388}{198}$$

Reduce the fraction \frac{388}{198} to lowest terms by extracting and canceling out 2.

$$\frac{194}{99}$$

Factor

$$\frac{2 \cdot 97}{3 ^ {2} \cdot 11} = 1\frac{95}{99} = 1.9595959595959596$$