Solve 1-frac{1/2/3-1-frac{2{3}}}{1-3/4}

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

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 2 to get 1.

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

Subtract 1 from 3 to get 2.

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

Convert 2 to fraction \frac{6}{3}.

$$\frac{\frac{\frac{1}{2}}{\frac{6}{3}-\frac{2}{3}}}{1-\frac{3}{4}}$$

Since \frac{6}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{1}{2}}{\frac{6-2}{3}}}{1-\frac{3}{4}}$$

Subtract 2 from 6 to get 4.

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

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

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

Multiply \frac{1}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 3}{2\times 4}.

$$\frac{\frac{3}{8}}{1-\frac{3}{4}}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{\frac{3}{8}}{\frac{4}{4}-\frac{3}{4}}$$

Since \frac{4}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{8}}{\frac{4-3}{4}}$$

Subtract 3 from 4 to get 1.

$$\frac{\frac{3}{8}}{\frac{1}{4}}$$

Divide \frac{3}{8} by \frac{1}{4} by multiplying \frac{3}{8} by the reciprocal of \frac{1}{4}.

$$\frac{3}{8}\times 4$$

Express \frac{3}{8}\times 4 as a single fraction.

$$\frac{3\times 4}{8}$$

Multiply 3 and 4 to get 12.

$$\frac{12}{8}$$

Reduce the fraction \frac{12}{8} to lowest terms by extracting and canceling out 4.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$