Solve (3/4-3/4:3/2+1/3)

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

Evaluate

$$\frac{7}{12}\approx 0.583333333$$

Solution Steps

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

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

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

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

Cancel out 3 in both numerator and denominator.

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

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

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

Subtract 2 from 3 to get 1.

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

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{1}{3} to fractions with denominator 12.

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

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

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

Add 3 and 4 to get 7.

$$\frac{7}{12}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 3} = 0.5833333333333334$$