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

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

Evaluate

$$\frac{1}{72}\approx 0.013888889$$

Solution Steps

Divide 3 by 3 to get 1.

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

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$\left(\frac{3}{6}+\frac{4}{6}-1\right)\left(2+\frac{1}{3}-\frac{2\times 4+1}{4}\right)$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\left(\frac{3+4}{6}-1\right)\left(2+\frac{1}{3}-\frac{2\times 4+1}{4}\right)$$

Add 3 and 4 to get 7.

$$\left(\frac{7}{6}-1\right)\left(2+\frac{1}{3}-\frac{2\times 4+1}{4}\right)$$

Convert 1 to fraction \frac{6}{6}.

$$\left(\frac{7}{6}-\frac{6}{6}\right)\left(2+\frac{1}{3}-\frac{2\times 4+1}{4}\right)$$

Since \frac{7}{6} and \frac{6}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-6}{6}\left(2+\frac{1}{3}-\frac{2\times 4+1}{4}\right)$$

Subtract 6 from 7 to get 1.

$$\frac{1}{6}\left(2+\frac{1}{3}-\frac{2\times 4+1}{4}\right)$$

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

$$\frac{1}{6}\left(\frac{6}{3}+\frac{1}{3}-\frac{2\times 4+1}{4}\right)$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{1}{6}\left(\frac{6+1}{3}-\frac{2\times 4+1}{4}\right)$$

Add 6 and 1 to get 7.

$$\frac{1}{6}\left(\frac{7}{3}-\frac{2\times 4+1}{4}\right)$$

Multiply 2 and 4 to get 8.

$$\frac{1}{6}\left(\frac{7}{3}-\frac{8+1}{4}\right)$$

Add 8 and 1 to get 9.

$$\frac{1}{6}\left(\frac{7}{3}-\frac{9}{4}\right)$$

Least common multiple of 3 and 4 is 12. Convert \frac{7}{3} and \frac{9}{4} to fractions with denominator 12.

$$\frac{1}{6}\left(\frac{28}{12}-\frac{27}{12}\right)$$

Since \frac{28}{12} and \frac{27}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}\times \frac{28-27}{12}$$

Subtract 27 from 28 to get 1.

$$\frac{1}{6}\times \frac{1}{12}$$

Multiply \frac{1}{6} times \frac{1}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{6\times 12}$$

Do the multiplications in the fraction \frac{1\times 1}{6\times 12}.

$$\frac{1}{72}$$

Factor

$$\frac{1}{2 ^ {3} \cdot 3 ^ {2}} = 0.013888888888888888$$