Solve 3/frac{3{2}}div13/4

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

Evaluate

$$\frac{8}{7}\approx 1.142857143$$

Solution Steps

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

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

Multiply 3 and 4 to get 12.

$$\frac{12}{\frac{3}{2}\left(1\times 4+3\right)}$$

Multiply 1 and 4 to get 4.

$$\frac{12}{\frac{3}{2}\left(4+3\right)}$$

Add 4 and 3 to get 7.

$$\frac{12}{\frac{3}{2}\times 7}$$

Express \frac{3}{2}\times 7 as a single fraction.

$$\frac{12}{\frac{3\times 7}{2}}$$

Multiply 3 and 7 to get 21.

$$\frac{12}{\frac{21}{2}}$$

Divide 12 by \frac{21}{2} by multiplying 12 by the reciprocal of \frac{21}{2}.

$$12\times \frac{2}{21}$$

Express 12\times \frac{2}{21} as a single fraction.

$$\frac{12\times 2}{21}$$

Multiply 12 and 2 to get 24.

$$\frac{24}{21}$$

Reduce the fraction \frac{24}{21} to lowest terms by extracting and canceling out 3.

$$\frac{8}{7}$$

Factor

$$\frac{2 ^ {3}}{7} = 1\frac{1}{7} = 1.1428571428571428$$