Solve (3/4-4/9)div5/6

$$( \frac { 3 } { 4 } - \frac { 4 } { 9 } ) \div \frac { 5 } { 6 }$$

Evaluate

$$\frac{11}{30}\approx 0.366666667$$

Solution Steps

Least common multiple of 4 and 9 is 36. Convert \frac{3}{4} and \frac{4}{9} to fractions with denominator 36.

$$\frac{\frac{27}{36}-\frac{16}{36}}{\frac{5}{6}}$$

Since \frac{27}{36} and \frac{16}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{27-16}{36}}{\frac{5}{6}}$$

Subtract 16 from 27 to get 11.

$$\frac{\frac{11}{36}}{\frac{5}{6}}$$

Divide \frac{11}{36} by \frac{5}{6} by multiplying \frac{11}{36} by the reciprocal of \frac{5}{6}.

$$\frac{11}{36}\times \frac{6}{5}$$

Multiply \frac{11}{36} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 6}{36\times 5}$$

Do the multiplications in the fraction \frac{11\times 6}{36\times 5}.

$$\frac{66}{180}$$

Reduce the fraction \frac{66}{180} to lowest terms by extracting and canceling out 6.

$$\frac{11}{30}$$

Factor

$$\frac{11}{2 \cdot 3 \cdot 5} = 0.36666666666666664$$