Solve (5/6+11/9):74/9

$$( \frac { 5 } { 6 } + \frac { 11 } { 9 } ) : \frac { 74 } { 9 }$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

Least common multiple of 6 and 9 is 18. Convert \frac{5}{6} and \frac{11}{9} to fractions with denominator 18.

$$\frac{\frac{15}{18}+\frac{22}{18}}{\frac{74}{9}}$$

Since \frac{15}{18} and \frac{22}{18} have the same denominator, add them by adding their numerators.

$$\frac{\frac{15+22}{18}}{\frac{74}{9}}$$

Add 15 and 22 to get 37.

$$\frac{\frac{37}{18}}{\frac{74}{9}}$$

Divide \frac{37}{18} by \frac{74}{9} by multiplying \frac{37}{18} by the reciprocal of \frac{74}{9}.

$$\frac{37}{18}\times \frac{9}{74}$$

Multiply \frac{37}{18} times \frac{9}{74} by multiplying numerator times numerator and denominator times denominator.

$$\frac{37\times 9}{18\times 74}$$

Do the multiplications in the fraction \frac{37\times 9}{18\times 74}.

$$\frac{333}{1332}$$

Reduce the fraction \frac{333}{1332} to lowest terms by extracting and canceling out 333.

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$