Solve 15/10*8/2:12/20*10/5:frac{20}{10}-frac{19}{2}-frac{9}{2}

$$\frac { 15 } { 10 } \cdot \frac { 8 } { 2 } : \frac { 12 } { 20 } \cdot \frac { 10 } { 5 } : \frac { 20 } { 10 } - \frac { 19 } { 2 } - \frac { 9 } { 2 }$$

Evaluate

$$-4$$

Solution Steps

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{\frac{3}{2}\times \frac{8}{2}}{\frac{12}{20}}\times \frac{10}{5}}{\frac{20}{10}}-\frac{19}{2}-\frac{9}{2}$$

Divide 8 by 2 to get 4.

$$\frac{\frac{\frac{3}{2}\times 4}{\frac{12}{20}}\times \frac{10}{5}}{\frac{20}{10}}-\frac{19}{2}-\frac{9}{2}$$

Express \frac{3}{2}\times 4 as a single fraction.

$$\frac{\frac{\frac{3\times 4}{2}}{\frac{12}{20}}\times \frac{10}{5}}{\frac{20}{10}}-\frac{19}{2}-\frac{9}{2}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{\frac{12}{2}}{\frac{12}{20}}\times \frac{10}{5}}{\frac{20}{10}}-\frac{19}{2}-\frac{9}{2}$$

Divide 12 by 2 to get 6.

$$\frac{\frac{6}{\frac{12}{20}}\times \frac{10}{5}}{\frac{20}{10}}-\frac{19}{2}-\frac{9}{2}$$

Reduce the fraction \frac{12}{20} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{6}{\frac{3}{5}}\times \frac{10}{5}}{\frac{20}{10}}-\frac{19}{2}-\frac{9}{2}$$

Divide 6 by \frac{3}{5} by multiplying 6 by the reciprocal of \frac{3}{5}.

$$\frac{6\times \frac{5}{3}\times \frac{10}{5}}{\frac{20}{10}}-\frac{19}{2}-\frac{9}{2}$$

Express 6\times \frac{5}{3} as a single fraction.

$$\frac{\frac{6\times 5}{3}\times \frac{10}{5}}{\frac{20}{10}}-\frac{19}{2}-\frac{9}{2}$$

Multiply 6 and 5 to get 30.

$$\frac{\frac{30}{3}\times \frac{10}{5}}{\frac{20}{10}}-\frac{19}{2}-\frac{9}{2}$$

Divide 30 by 3 to get 10.

$$\frac{10\times \frac{10}{5}}{\frac{20}{10}}-\frac{19}{2}-\frac{9}{2}$$

Divide 10 by 5 to get 2.

$$\frac{10\times 2}{\frac{20}{10}}-\frac{19}{2}-\frac{9}{2}$$

Multiply 10 and 2 to get 20.

$$\frac{20}{\frac{20}{10}}-\frac{19}{2}-\frac{9}{2}$$

Divide 20 by 10 to get 2.

$$\frac{20}{2}-\frac{19}{2}-\frac{9}{2}$$

Since \frac{20}{2} and \frac{19}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-19}{2}-\frac{9}{2}$$

Subtract 19 from 20 to get 1.

$$\frac{1}{2}-\frac{9}{2}$$

Since \frac{1}{2} and \frac{9}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-9}{2}$$

Subtract 9 from 1 to get -8.

$$\frac{-8}{2}$$

Divide -8 by 2 to get -4.

$$-4$$

Factor

$$-4$$