Solve (1/2div3/4)div3/2

$$( \frac { 1 } { 2 } \div \frac { 3 } { 4 } ) \div \frac { 3 } { 2 }$$

Evaluate

$$\frac{4}{9}\approx 0.444444444$$

Solution Steps

Divide \frac{\frac{1}{2}}{\frac{3}{4}} by \frac{3}{2} by multiplying \frac{\frac{1}{2}}{\frac{3}{4}} by the reciprocal of \frac{3}{2}.

$$\frac{\frac{1}{2}\times 2}{\frac{3}{4}\times 3}$$

Cancel out 2 and 2.

$$\frac{1}{\frac{3}{4}\times 3}$$

Express \frac{3}{4}\times 3 as a single fraction.

$$\frac{1}{\frac{3\times 3}{4}}$$

Multiply 3 and 3 to get 9.

$$\frac{1}{\frac{9}{4}}$$

Divide 1 by \frac{9}{4} by multiplying 1 by the reciprocal of \frac{9}{4}.

$$1\times \frac{4}{9}$$

Multiply 1 and \frac{4}{9} to get \frac{4}{9}.

$$\frac{4}{9}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {2}} = 0.4444444444444444$$