Solve 3/2div1/4div2/5div3/2divfrac{1}{4}divfrac{2}{5}=

$$\frac { 3 } { 2 } \div \frac { 1 } { 4 } \div \frac { 2 } { 5 } \div \frac { 3 } { 2 } \div \frac { 1 } { 4 } \div \frac { 2 } { 5 } =$$

Evaluate

$$100$$

Solution Steps

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

$$\frac{\frac{\frac{\frac{\frac{3}{2}}{\frac{1}{4}}}{\frac{2}{5}}}{\frac{3}{2}}\times 5}{\frac{1}{4}\times 2}$$

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

$$\frac{\frac{\frac{\frac{3}{2}}{\frac{1}{4}}\times 2}{\frac{2}{5}\times 3}\times 5}{\frac{1}{4}\times 2}$$

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

$$\frac{\frac{\frac{3}{2}\times 4\times 2}{\frac{2}{5}\times 3}\times 5}{\frac{1}{4}\times 2}$$

Express \frac{3}{2}\times 4 as a single fraction.

$$\frac{\frac{\frac{3\times 4}{2}\times 2}{\frac{2}{5}\times 3}\times 5}{\frac{1}{4}\times 2}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{\frac{12}{2}\times 2}{\frac{2}{5}\times 3}\times 5}{\frac{1}{4}\times 2}$$

Divide 12 by 2 to get 6.

$$\frac{\frac{6\times 2}{\frac{2}{5}\times 3}\times 5}{\frac{1}{4}\times 2}$$

Multiply 6 and 2 to get 12.

$$\frac{\frac{12}{\frac{2}{5}\times 3}\times 5}{\frac{1}{4}\times 2}$$

Express \frac{2}{5}\times 3 as a single fraction.

$$\frac{\frac{12}{\frac{2\times 3}{5}}\times 5}{\frac{1}{4}\times 2}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{12}{\frac{6}{5}}\times 5}{\frac{1}{4}\times 2}$$

Divide 12 by \frac{6}{5} by multiplying 12 by the reciprocal of \frac{6}{5}.

$$\frac{12\times \frac{5}{6}\times 5}{\frac{1}{4}\times 2}$$

Express 12\times \frac{5}{6} as a single fraction.

$$\frac{\frac{12\times 5}{6}\times 5}{\frac{1}{4}\times 2}$$

Multiply 12 and 5 to get 60.

$$\frac{\frac{60}{6}\times 5}{\frac{1}{4}\times 2}$$

Divide 60 by 6 to get 10.

$$\frac{10\times 5}{\frac{1}{4}\times 2}$$

Multiply 10 and 5 to get 50.

$$\frac{50}{\frac{1}{4}\times 2}$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$\frac{50}{\frac{2}{4}}$$

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

$$\frac{50}{\frac{1}{2}}$$

Divide 50 by \frac{1}{2} by multiplying 50 by the reciprocal of \frac{1}{2}.

$$50\times 2$$

Multiply 50 and 2 to get 100.

$$100$$

Factor

$$2^{2}\times 5^{2}$$