Solve 11/10-10/11/frac{10{11}}*100

$$\frac { \frac { 11 } { 10 } - \frac { 10 } { 11 } } { \frac { 10 } { 11 } } \times 100$$

Evaluate

$$21$$

Solution Steps

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

$$\frac{\frac{121}{110}-\frac{100}{110}}{\frac{10}{11}}\times 100$$

Since \frac{121}{110} and \frac{100}{110} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{121-100}{110}}{\frac{10}{11}}\times 100$$

Subtract 100 from 121 to get 21.

$$\frac{\frac{21}{110}}{\frac{10}{11}}\times 100$$

Divide \frac{21}{110} by \frac{10}{11} by multiplying \frac{21}{110} by the reciprocal of \frac{10}{11}.

$$\frac{21}{110}\times \frac{11}{10}\times 100$$

Multiply \frac{21}{110} times \frac{11}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21\times 11}{110\times 10}\times 100$$

Do the multiplications in the fraction \frac{21\times 11}{110\times 10}.

$$\frac{231}{1100}\times 100$$

Reduce the fraction \frac{231}{1100} to lowest terms by extracting and canceling out 11.

$$\frac{21}{100}\times 100$$

Cancel out 100 and 100.

$$21$$

Factor

$$3\times 7$$