Solve 75/6-(1/4)(9/3)/frac{3{5}(frac{7}{4})+(frac{3}{7}}

$$\frac { 7 \frac { 5 } { 6 } - ( \frac { 1 } { 4 } ) ( \frac { 9 } { 3 } ) } { \frac { 3 } { 5 } ( \frac { 7 } { 4 } ) + ( \frac { 3 } { 7 } }$$

Evaluate

$$\frac{2975}{621}\approx 4.790660225$$

Solution Steps

Multiply 7 and 6 to get 42.

$$\frac{\frac{42+5}{6}-\frac{1}{4}\times \frac{9}{3}}{\frac{3}{5}\times \frac{7}{4}+\frac{3}{7}}$$

Add 42 and 5 to get 47.

$$\frac{\frac{47}{6}-\frac{1}{4}\times \frac{9}{3}}{\frac{3}{5}\times \frac{7}{4}+\frac{3}{7}}$$

Divide 9 by 3 to get 3.

$$\frac{\frac{47}{6}-\frac{1}{4}\times 3}{\frac{3}{5}\times \frac{7}{4}+\frac{3}{7}}$$

Multiply \frac{1}{4} and 3 to get \frac{3}{4}.

$$\frac{\frac{47}{6}-\frac{3}{4}}{\frac{3}{5}\times \frac{7}{4}+\frac{3}{7}}$$

Least common multiple of 6 and 4 is 12. Convert \frac{47}{6} and \frac{3}{4} to fractions with denominator 12.

$$\frac{\frac{94}{12}-\frac{9}{12}}{\frac{3}{5}\times \frac{7}{4}+\frac{3}{7}}$$

Since \frac{94}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{94-9}{12}}{\frac{3}{5}\times \frac{7}{4}+\frac{3}{7}}$$

Subtract 9 from 94 to get 85.

$$\frac{\frac{85}{12}}{\frac{3}{5}\times \frac{7}{4}+\frac{3}{7}}$$

Multiply \frac{3}{5} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{85}{12}}{\frac{3\times 7}{5\times 4}+\frac{3}{7}}$$

Do the multiplications in the fraction \frac{3\times 7}{5\times 4}.

$$\frac{\frac{85}{12}}{\frac{21}{20}+\frac{3}{7}}$$

Least common multiple of 20 and 7 is 140. Convert \frac{21}{20} and \frac{3}{7} to fractions with denominator 140.

$$\frac{\frac{85}{12}}{\frac{147}{140}+\frac{60}{140}}$$

Since \frac{147}{140} and \frac{60}{140} have the same denominator, add them by adding their numerators.

$$\frac{\frac{85}{12}}{\frac{147+60}{140}}$$

Add 147 and 60 to get 207.

$$\frac{\frac{85}{12}}{\frac{207}{140}}$$

Divide \frac{85}{12} by \frac{207}{140} by multiplying \frac{85}{12} by the reciprocal of \frac{207}{140}.

$$\frac{85}{12}\times \frac{140}{207}$$

Multiply \frac{85}{12} times \frac{140}{207} by multiplying numerator times numerator and denominator times denominator.

$$\frac{85\times 140}{12\times 207}$$

Do the multiplications in the fraction \frac{85\times 140}{12\times 207}.

$$\frac{11900}{2484}$$

Reduce the fraction \frac{11900}{2484} to lowest terms by extracting and canceling out 4.

$$\frac{2975}{621}$$

Factor

$$\frac{5 ^ {2} \cdot 7 \cdot 17}{3 ^ {3} \cdot 23} = 4\frac{491}{621} = 4.790660225442834$$