Solve 11/4+(22/3*13/4-31/6div7frac{3}{5})

$$1 \frac { 1 } { 4 } + ( 2 \frac { 2 } { 3 } \times 1 \frac { 3 } { 4 } - 3 \frac { 1 } { 6 } \div 7 \frac { 3 } { 5 } )$$

Evaluate

$$\frac{11}{2}=5.5$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{4+1}{4}+\frac{2\times 3+2}{3}\times \frac{1\times 4+3}{4}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Add 4 and 1 to get 5.

$$\frac{5}{4}+\frac{2\times 3+2}{3}\times \frac{1\times 4+3}{4}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Multiply 2 and 3 to get 6.

$$\frac{5}{4}+\frac{6+2}{3}\times \frac{1\times 4+3}{4}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Add 6 and 2 to get 8.

$$\frac{5}{4}+\frac{8}{3}\times \frac{1\times 4+3}{4}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Multiply 1 and 4 to get 4.

$$\frac{5}{4}+\frac{8}{3}\times \frac{4+3}{4}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Add 4 and 3 to get 7.

$$\frac{5}{4}+\frac{8}{3}\times \frac{7}{4}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Multiply \frac{8}{3} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{4}+\frac{8\times 7}{3\times 4}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Do the multiplications in the fraction \frac{8\times 7}{3\times 4}.

$$\frac{5}{4}+\frac{56}{12}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Reduce the fraction \frac{56}{12} to lowest terms by extracting and canceling out 4.

$$\frac{5}{4}+\frac{14}{3}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Least common multiple of 4 and 3 is 12. Convert \frac{5}{4} and \frac{14}{3} to fractions with denominator 12.

$$\frac{15}{12}+\frac{56}{12}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Since \frac{15}{12} and \frac{56}{12} have the same denominator, add them by adding their numerators.

$$\frac{15+56}{12}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Add 15 and 56 to get 71.

$$\frac{71}{12}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Divide \frac{3\times 6+1}{6} by \frac{7\times 5+3}{5} by multiplying \frac{3\times 6+1}{6} by the reciprocal of \frac{7\times 5+3}{5}.

$$\frac{71}{12}-\frac{\left(3\times 6+1\right)\times 5}{6\left(7\times 5+3\right)}$$

Multiply 3 and 6 to get 18.

$$\frac{71}{12}-\frac{\left(18+1\right)\times 5}{6\left(7\times 5+3\right)}$$

Add 18 and 1 to get 19.

$$\frac{71}{12}-\frac{19\times 5}{6\left(7\times 5+3\right)}$$

Multiply 19 and 5 to get 95.

$$\frac{71}{12}-\frac{95}{6\left(7\times 5+3\right)}$$

Multiply 7 and 5 to get 35.

$$\frac{71}{12}-\frac{95}{6\left(35+3\right)}$$

Add 35 and 3 to get 38.

$$\frac{71}{12}-\frac{95}{6\times 38}$$

Multiply 6 and 38 to get 228.

$$\frac{71}{12}-\frac{95}{228}$$

Reduce the fraction \frac{95}{228} to lowest terms by extracting and canceling out 19.

$$\frac{71}{12}-\frac{5}{12}$$

Since \frac{71}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{71-5}{12}$$

Subtract 5 from 71 to get 66.

$$\frac{66}{12}$$

Reduce the fraction \frac{66}{12} to lowest terms by extracting and canceling out 6.

$$\frac{11}{2}$$

Factor

$$\frac{11}{2} = 5\frac{1}{2} = 5.5$$