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

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

Evaluate

$$\frac{41}{12}\approx 3.416666667$$

Solution Steps

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

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

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

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

Add 2 and 1 to get 3.

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

Convert 3 to fraction \frac{12}{4}.

$$2+\frac{\frac{3}{2}}{\frac{12}{4}-\frac{3}{4}}+\frac{3}{4}$$

Since \frac{12}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$2+\frac{\frac{3}{2}}{\frac{12-3}{4}}+\frac{3}{4}$$

Subtract 3 from 12 to get 9.

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

Divide \frac{3}{2} by \frac{9}{4} by multiplying \frac{3}{2} by the reciprocal of \frac{9}{4}.

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

Multiply \frac{3}{2} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{3\times 4}{2\times 9}.

$$2+\frac{12}{18}+\frac{3}{4}$$

Reduce the fraction \frac{12}{18} to lowest terms by extracting and canceling out 6.

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

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

$$\frac{6}{3}+\frac{2}{3}+\frac{3}{4}$$

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

$$\frac{6+2}{3}+\frac{3}{4}$$

Add 6 and 2 to get 8.

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

Least common multiple of 3 and 4 is 12. Convert \frac{8}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{32}{12}+\frac{9}{12}$$

Since \frac{32}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{32+9}{12}$$

Add 32 and 9 to get 41.

$$\frac{41}{12}$$

Factor

$$\frac{41}{2 ^ {2} \cdot 3} = 3\frac{5}{12} = 3.4166666666666665$$