Solve (3/4text{of}4/9div91/2)div15/19

$$( \frac { 3 } { 4 } \text { of } \frac { 4 } { 9 } \div 9 \frac { 1 } { 2 } ) \div 1 \frac { 5 } { 19 }$$

Evaluate

$$\frac{1}{36}\approx 0.027777778$$

Solution Steps

Divide \frac{\frac{3}{4}\times \frac{4}{9}}{\frac{9\times 2+1}{2}} by \frac{1\times 19+5}{19} by multiplying \frac{\frac{3}{4}\times \frac{4}{9}}{\frac{9\times 2+1}{2}} by the reciprocal of \frac{1\times 19+5}{19}.

$$\frac{\frac{3}{4}\times \frac{4}{9}\times 19}{\frac{9\times 2+1}{2}\left(1\times 19+5\right)}$$

Multiply \frac{3}{4} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 4}{4\times 9}\times 19}{\frac{9\times 2+1}{2}\left(1\times 19+5\right)}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{3}{9}\times 19}{\frac{9\times 2+1}{2}\left(1\times 19+5\right)}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{3}\times 19}{\frac{9\times 2+1}{2}\left(1\times 19+5\right)}$$

Multiply \frac{1}{3} and 19 to get \frac{19}{3}.

$$\frac{\frac{19}{3}}{\frac{9\times 2+1}{2}\left(1\times 19+5\right)}$$

Multiply 9 and 2 to get 18.

$$\frac{\frac{19}{3}}{\frac{18+1}{2}\left(1\times 19+5\right)}$$

Add 18 and 1 to get 19.

$$\frac{\frac{19}{3}}{\frac{19}{2}\left(1\times 19+5\right)}$$

Multiply 1 and 19 to get 19.

$$\frac{\frac{19}{3}}{\frac{19}{2}\left(19+5\right)}$$

Add 19 and 5 to get 24.

$$\frac{\frac{19}{3}}{\frac{19}{2}\times 24}$$

Express \frac{19}{2}\times 24 as a single fraction.

$$\frac{\frac{19}{3}}{\frac{19\times 24}{2}}$$

Multiply 19 and 24 to get 456.

$$\frac{\frac{19}{3}}{\frac{456}{2}}$$

Divide 456 by 2 to get 228.

$$\frac{\frac{19}{3}}{228}$$

Express \frac{\frac{19}{3}}{228} as a single fraction.

$$\frac{19}{3\times 228}$$

Multiply 3 and 228 to get 684.

$$\frac{19}{684}$$

Reduce the fraction \frac{19}{684} to lowest terms by extracting and canceling out 19.

$$\frac{1}{36}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 3 ^ {2}} = 0.027777777777777776$$