Solve (11/10-4/11):15/44

$$( \frac { 11 } { 10 } - \frac { 4 } { 11 } ) : \frac { 15 } { 44 }$$

Evaluate

$$\frac{54}{25}=2.16$$

Solution Steps

Least common multiple of 10 and 11 is 110. Convert \frac{11}{10} and \frac{4}{11} to fractions with denominator 110.

$$\frac{\frac{121}{110}-\frac{40}{110}}{\frac{15}{44}}$$

Since \frac{121}{110} and \frac{40}{110} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{121-40}{110}}{\frac{15}{44}}$$

Subtract 40 from 121 to get 81.

$$\frac{\frac{81}{110}}{\frac{15}{44}}$$

Divide \frac{81}{110} by \frac{15}{44} by multiplying \frac{81}{110} by the reciprocal of \frac{15}{44}.

$$\frac{81}{110}\times \frac{44}{15}$$

Multiply \frac{81}{110} times \frac{44}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{81\times 44}{110\times 15}$$

Do the multiplications in the fraction \frac{81\times 44}{110\times 15}.

$$\frac{3564}{1650}$$

Reduce the fraction \frac{3564}{1650} to lowest terms by extracting and canceling out 66.

$$\frac{54}{25}$$

Factor

$$\frac{2 \cdot 3 ^ {3}}{5 ^ {2}} = 2\frac{4}{25} = 2.16$$