Solve 23/7*3/17-3/5div(6frac{4/5-5frac{2}{5})}{4frac{4}{5}div1frac{1}{2}-3}

$$\frac{ 2 \frac { 3 } { 7 } \times \frac{ 3 }{ 17 } - \frac{ 3 }{ 5 } \div ( 6 \frac { 4 } { 5 } - 5 \frac { 2 } { 5 } ) }{ 4 \frac { 4 } { 5 } \div 1 \frac { 1 } { 2 } -3 }$$

Evaluate

$$0$$

Solution Steps

Multiply 2 and 7 to get 14.

$$\frac{\frac{14+3}{7}\times \frac{3}{17}-\frac{\frac{3}{5}}{\frac{6\times 5+4}{5}-\frac{5\times 5+2}{5}}}{\frac{\frac{4\times 5+4}{5}}{\frac{1\times 2+1}{2}}-3}$$

Add 14 and 3 to get 17.

$$\frac{\frac{17}{7}\times \frac{3}{17}-\frac{\frac{3}{5}}{\frac{6\times 5+4}{5}-\frac{5\times 5+2}{5}}}{\frac{\frac{4\times 5+4}{5}}{\frac{1\times 2+1}{2}}-3}$$

Multiply \frac{17}{7} times \frac{3}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{17\times 3}{7\times 17}-\frac{\frac{3}{5}}{\frac{6\times 5+4}{5}-\frac{5\times 5+2}{5}}}{\frac{\frac{4\times 5+4}{5}}{\frac{1\times 2+1}{2}}-3}$$

Cancel out 17 in both numerator and denominator.

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

Multiply 6 and 5 to get 30.

$$\frac{\frac{3}{7}-\frac{\frac{3}{5}}{\frac{30+4}{5}-\frac{5\times 5+2}{5}}}{\frac{\frac{4\times 5+4}{5}}{\frac{1\times 2+1}{2}}-3}$$

Add 30 and 4 to get 34.

$$\frac{\frac{3}{7}-\frac{\frac{3}{5}}{\frac{34}{5}-\frac{5\times 5+2}{5}}}{\frac{\frac{4\times 5+4}{5}}{\frac{1\times 2+1}{2}}-3}$$

Multiply 5 and 5 to get 25.

$$\frac{\frac{3}{7}-\frac{\frac{3}{5}}{\frac{34}{5}-\frac{25+2}{5}}}{\frac{\frac{4\times 5+4}{5}}{\frac{1\times 2+1}{2}}-3}$$

Add 25 and 2 to get 27.

$$\frac{\frac{3}{7}-\frac{\frac{3}{5}}{\frac{34}{5}-\frac{27}{5}}}{\frac{\frac{4\times 5+4}{5}}{\frac{1\times 2+1}{2}}-3}$$

Since \frac{34}{5} and \frac{27}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{7}-\frac{\frac{3}{5}}{\frac{34-27}{5}}}{\frac{\frac{4\times 5+4}{5}}{\frac{1\times 2+1}{2}}-3}$$

Subtract 27 from 34 to get 7.

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

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

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

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

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

Cancel out 5 in both numerator and denominator.

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

Subtract \frac{3}{7} from \frac{3}{7} to get 0.

$$\frac{0}{\frac{\frac{4\times 5+4}{5}}{\frac{1\times 2+1}{2}}-3}$$

Divide \frac{4\times 5+4}{5} by \frac{1\times 2+1}{2} by multiplying \frac{4\times 5+4}{5} by the reciprocal of \frac{1\times 2+1}{2}.

$$\frac{0}{\frac{\left(4\times 5+4\right)\times 2}{5\left(1\times 2+1\right)}-3}$$

Multiply 4 and 5 to get 20.

$$\frac{0}{\frac{\left(20+4\right)\times 2}{5\left(1\times 2+1\right)}-3}$$

Add 20 and 4 to get 24.

$$\frac{0}{\frac{24\times 2}{5\left(1\times 2+1\right)}-3}$$

Multiply 24 and 2 to get 48.

$$\frac{0}{\frac{48}{5\left(1\times 2+1\right)}-3}$$

Multiply 1 and 2 to get 2.

$$\frac{0}{\frac{48}{5\left(2+1\right)}-3}$$

Add 2 and 1 to get 3.

$$\frac{0}{\frac{48}{5\times 3}-3}$$

Multiply 5 and 3 to get 15.

$$\frac{0}{\frac{48}{15}-3}$$

Reduce the fraction \frac{48}{15} to lowest terms by extracting and canceling out 3.

$$\frac{0}{\frac{16}{5}-3}$$

Convert 3 to fraction \frac{15}{5}.

$$\frac{0}{\frac{16}{5}-\frac{15}{5}}$$

Since \frac{16}{5} and \frac{15}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{0}{\frac{16-15}{5}}$$

Subtract 15 from 16 to get 1.

$$\frac{0}{\frac{1}{5}}$$

Zero divided by any non-zero number gives zero.

$$0$$

Factor

$$0$$