Solve (31/4div4/9)div1/2

$$( 3 \frac { 1 } { 4 } \div \frac { 4 } { 9 } ) \div \frac { 1 } { 2 }$$

Evaluate

$$\frac{117}{8}=14.625$$

Solution Steps

Divide \frac{\frac{3\times 4+1}{4}}{\frac{4}{9}} by \frac{1}{2} by multiplying \frac{\frac{3\times 4+1}{4}}{\frac{4}{9}} by the reciprocal of \frac{1}{2}.

$$\frac{\frac{3\times 4+1}{4}\times 2}{\frac{4}{9}}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{12+1}{4}\times 2}{\frac{4}{9}}$$

Add 12 and 1 to get 13.

$$\frac{\frac{13}{4}\times 2}{\frac{4}{9}}$$

Express \frac{13}{4}\times 2 as a single fraction.

$$\frac{\frac{13\times 2}{4}}{\frac{4}{9}}$$

Multiply 13 and 2 to get 26.

$$\frac{\frac{26}{4}}{\frac{4}{9}}$$

Reduce the fraction \frac{26}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{13}{2}}{\frac{4}{9}}$$

Divide \frac{13}{2} by \frac{4}{9} by multiplying \frac{13}{2} by the reciprocal of \frac{4}{9}.

$$\frac{13}{2}\times \frac{9}{4}$$

Multiply \frac{13}{2} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 9}{2\times 4}$$

Do the multiplications in the fraction \frac{13\times 9}{2\times 4}.

$$\frac{117}{8}$$

Factor

$$\frac{3 ^ {2} \cdot 13}{2 ^ {3}} = 14\frac{5}{8} = 14.625$$