Solve 22/9div5/6

$$2 \frac { 2 } { 9 } \div \frac { 5 } { 6 }$$

Evaluate

$$\frac{8}{3}\approx 2.666666667$$

Solution Steps

Divide \frac{2\times 9+2}{9} by \frac{5}{6} by multiplying \frac{2\times 9+2}{9} by the reciprocal of \frac{5}{6}.

$$\frac{\left(2\times 9+2\right)\times 6}{9\times 5}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\left(2+2\times 9\right)}{3\times 5}$$

Multiply 2 and 9 to get 18.

$$\frac{2\left(2+18\right)}{3\times 5}$$

Add 2 and 18 to get 20.

$$\frac{2\times 20}{3\times 5}$$

Multiply 2 and 20 to get 40.

$$\frac{40}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{40}{15}$$

Reduce the fraction \frac{40}{15} to lowest terms by extracting and canceling out 5.

$$\frac{8}{3}$$

Factor

$$\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2.6666666666666665$$