Solve 15/28*(75/7:33/5-1/7)+5frac{5}{6}:frac{5}{12}

$$1 \frac { 5 } { 28 } \cdot ( 7 \frac { 5 } { 7 } : 3 \frac { 3 } { 5 } - \frac { 1 } { 7 } ) + 5 \frac { 5 } { 6 } : \frac { 5 } { 12 }$$

Evaluate

$$\frac{229}{14}\approx 16.357142857$$

Solution Steps

Multiply 1 and 28 to get 28.

$$\frac{28+5}{28}\left(\frac{\frac{7\times 7+5}{7}}{\frac{3\times 5+3}{5}}-\frac{1}{7}\right)+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

Add 28 and 5 to get 33.

$$\frac{33}{28}\left(\frac{\frac{7\times 7+5}{7}}{\frac{3\times 5+3}{5}}-\frac{1}{7}\right)+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

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

$$\frac{33}{28}\left(\frac{\left(7\times 7+5\right)\times 5}{7\left(3\times 5+3\right)}-\frac{1}{7}\right)+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

Multiply 7 and 7 to get 49.

$$\frac{33}{28}\left(\frac{\left(49+5\right)\times 5}{7\left(3\times 5+3\right)}-\frac{1}{7}\right)+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

Add 49 and 5 to get 54.

$$\frac{33}{28}\left(\frac{54\times 5}{7\left(3\times 5+3\right)}-\frac{1}{7}\right)+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

Multiply 54 and 5 to get 270.

$$\frac{33}{28}\left(\frac{270}{7\left(3\times 5+3\right)}-\frac{1}{7}\right)+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

Multiply 3 and 5 to get 15.

$$\frac{33}{28}\left(\frac{270}{7\left(15+3\right)}-\frac{1}{7}\right)+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

Add 15 and 3 to get 18.

$$\frac{33}{28}\left(\frac{270}{7\times 18}-\frac{1}{7}\right)+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

Multiply 7 and 18 to get 126.

$$\frac{33}{28}\left(\frac{270}{126}-\frac{1}{7}\right)+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

Reduce the fraction \frac{270}{126} to lowest terms by extracting and canceling out 18.

$$\frac{33}{28}\left(\frac{15}{7}-\frac{1}{7}\right)+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

Since \frac{15}{7} and \frac{1}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{33}{28}\times \frac{15-1}{7}+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

Subtract 1 from 15 to get 14.

$$\frac{33}{28}\times \frac{14}{7}+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

Divide 14 by 7 to get 2.

$$\frac{33}{28}\times 2+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

Express \frac{33}{28}\times 2 as a single fraction.

$$\frac{33\times 2}{28}+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

Multiply 33 and 2 to get 66.

$$\frac{66}{28}+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

Reduce the fraction \frac{66}{28} to lowest terms by extracting and canceling out 2.

$$\frac{33}{14}+\frac{\frac{5\times 6+5}{6}}{\frac{5}{12}}$$

Divide \frac{5\times 6+5}{6} by \frac{5}{12} by multiplying \frac{5\times 6+5}{6} by the reciprocal of \frac{5}{12}.

$$\frac{33}{14}+\frac{\left(5\times 6+5\right)\times 12}{6\times 5}$$

Cancel out 6 in both numerator and denominator.

$$\frac{33}{14}+\frac{2\left(5+5\times 6\right)}{5}$$

Multiply 5 and 6 to get 30.

$$\frac{33}{14}+\frac{2\left(5+30\right)}{5}$$

Add 5 and 30 to get 35.

$$\frac{33}{14}+\frac{2\times 35}{5}$$

Multiply 2 and 35 to get 70.

$$\frac{33}{14}+\frac{70}{5}$$

Divide 70 by 5 to get 14.

$$\frac{33}{14}+14$$

Convert 14 to fraction \frac{196}{14}.

$$\frac{33}{14}+\frac{196}{14}$$

Since \frac{33}{14} and \frac{196}{14} have the same denominator, add them by adding their numerators.

$$\frac{33+196}{14}$$

Add 33 and 196 to get 229.

$$\frac{229}{14}$$

Factor

$$\frac{229}{2 \cdot 7} = 16\frac{5}{14} = 16.357142857142858$$