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

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

Evaluate

$$\frac{9}{44}\approx 0.204545455$$

Solution Steps

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

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

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

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

Subtract 3 from 4 to get 1.

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

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

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

Since \frac{1}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

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

Add 1 and 2 to get 3.

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

Convert 3 to fraction \frac{9}{3}.

$$\frac{\frac{3}{4}}{\frac{2}{3}+\frac{9}{3}}$$

Since \frac{2}{3} and \frac{9}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{4}}{\frac{2+9}{3}}$$

Add 2 and 9 to get 11.

$$\frac{\frac{3}{4}}{\frac{11}{3}}$$

Divide \frac{3}{4} by \frac{11}{3} by multiplying \frac{3}{4} by the reciprocal of \frac{11}{3}.

$$\frac{3}{4}\times \frac{3}{11}$$

Multiply \frac{3}{4} times \frac{3}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 3}{4\times 11}$$

Do the multiplications in the fraction \frac{3\times 3}{4\times 11}.

$$\frac{9}{44}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2} \cdot 11} = 0.20454545454545456$$