Solve (11/10+1/11)-(111/10*1/11)

$$( \frac{ 11 }{ 10 } + \frac{ 1 }{ 11 } )-( \frac{ 111 }{ 10 } \times \frac{ 1 }{ 11 } )$$

Evaluate

$$\frac{2}{11}\approx 0.181818182$$

Solution Steps

Least common multiple of 10 and 11 is 110. Convert \frac{11}{10} and \frac{1}{11} to fractions with denominator 110.

$$\frac{121}{110}+\frac{10}{110}-\frac{111}{10}\times \frac{1}{11}$$

Since \frac{121}{110} and \frac{10}{110} have the same denominator, add them by adding their numerators.

$$\frac{121+10}{110}-\frac{111}{10}\times \frac{1}{11}$$

Add 121 and 10 to get 131.

$$\frac{131}{110}-\frac{111}{10}\times \frac{1}{11}$$

Multiply \frac{111}{10} times \frac{1}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{131}{110}-\frac{111\times 1}{10\times 11}$$

Do the multiplications in the fraction \frac{111\times 1}{10\times 11}.

$$\frac{131}{110}-\frac{111}{110}$$

Since \frac{131}{110} and \frac{111}{110} have the same denominator, subtract them by subtracting their numerators.

$$\frac{131-111}{110}$$

Subtract 111 from 131 to get 20.

$$\frac{20}{110}$$

Reduce the fraction \frac{20}{110} to lowest terms by extracting and canceling out 10.

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

Factor

$$\frac{2}{11} = 0.18181818181818182$$