Solve 121/10-(22/5-13/10)div21/5

$$\frac{ 121 }{ 10 } -( 2 \frac { 2 } { 5 } - 1 \frac { 3 } { 10 } ) \div 2 \frac { 1 } { 5 }$$

Evaluate

$$\frac{58}{5}=11.6$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{121}{10}-\frac{\frac{10+2}{5}-\frac{1\times 10+3}{10}}{\frac{2\times 5+1}{5}}$$

Add 10 and 2 to get 12.

$$\frac{121}{10}-\frac{\frac{12}{5}-\frac{1\times 10+3}{10}}{\frac{2\times 5+1}{5}}$$

Multiply 1 and 10 to get 10.

$$\frac{121}{10}-\frac{\frac{12}{5}-\frac{10+3}{10}}{\frac{2\times 5+1}{5}}$$

Add 10 and 3 to get 13.

$$\frac{121}{10}-\frac{\frac{12}{5}-\frac{13}{10}}{\frac{2\times 5+1}{5}}$$

Least common multiple of 5 and 10 is 10. Convert \frac{12}{5} and \frac{13}{10} to fractions with denominator 10.

$$\frac{121}{10}-\frac{\frac{24}{10}-\frac{13}{10}}{\frac{2\times 5+1}{5}}$$

Since \frac{24}{10} and \frac{13}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{121}{10}-\frac{\frac{24-13}{10}}{\frac{2\times 5+1}{5}}$$

Subtract 13 from 24 to get 11.

$$\frac{121}{10}-\frac{\frac{11}{10}}{\frac{2\times 5+1}{5}}$$

Multiply 2 and 5 to get 10.

$$\frac{121}{10}-\frac{\frac{11}{10}}{\frac{10+1}{5}}$$

Add 10 and 1 to get 11.

$$\frac{121}{10}-\frac{\frac{11}{10}}{\frac{11}{5}}$$

Divide \frac{11}{10} by \frac{11}{5} by multiplying \frac{11}{10} by the reciprocal of \frac{11}{5}.

$$\frac{121}{10}-\frac{11}{10}\times \frac{5}{11}$$

Multiply \frac{11}{10} times \frac{5}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{121}{10}-\frac{11\times 5}{10\times 11}$$

Cancel out 11 in both numerator and denominator.

$$\frac{121}{10}-\frac{5}{10}$$

Since \frac{121}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{121-5}{10}$$

Subtract 5 from 121 to get 116.

$$\frac{116}{10}$$

Reduce the fraction \frac{116}{10} to lowest terms by extracting and canceling out 2.

$$\frac{58}{5}$$

Factor

$$\frac{2 \cdot 29}{5} = 11\frac{3}{5} = 11.6$$