Solve 3/4-1/2/1+frac{3{4}(1/2)}

$$\frac { \frac { 3 } { 4 } - \frac { 1 } { 2 } } { 1 + \frac { 3 } { 4 } ( \frac { 1 } { 2 } ) }$$

Evaluate

$$\frac{2}{11}\approx 0.181818182$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

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

Since \frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 3 to get 1.

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

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

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

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

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

Convert 1 to fraction \frac{8}{8}.

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

Since \frac{8}{8} and \frac{3}{8} have the same denominator, add them by adding their numerators.

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

Add 8 and 3 to get 11.

$$\frac{\frac{1}{4}}{\frac{11}{8}}$$

Divide \frac{1}{4} by \frac{11}{8} by multiplying \frac{1}{4} by the reciprocal of \frac{11}{8}.

$$\frac{1}{4}\times \frac{8}{11}$$

Multiply \frac{1}{4} times \frac{8}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 8}{4\times 11}$$

Do the multiplications in the fraction \frac{1\times 8}{4\times 11}.

$$\frac{8}{44}$$

Reduce the fraction \frac{8}{44} to lowest terms by extracting and canceling out 4.

$$\frac{2}{11}$$

Factor

$$\frac{2}{11} = 0.18181818181818182$$