Solve -3216/25div(-8*4)+25^2+(1/2+2/3-3/4-frac{11}{12})*24

$$- 32 \frac { 16 } { 25 } \div ( - 8 \times 4 ) + 25 ^ { 2 } + ( \frac { 1 } { 2 } + \frac { 2 } { 3 } - \frac { 3 } { 4 } - \frac { 11 } { 12 } ) \times 24$$

Evaluate

$$\frac{30701}{50}=614.02$$

Solution Steps

Multiply 32 and 25 to get 800.

$$\frac{-\frac{800+16}{25}}{-8\times 4}+25^{2}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Add 800 and 16 to get 816.

$$\frac{-\frac{816}{25}}{-8\times 4}+25^{2}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Multiply -8 and 4 to get -32.

$$\frac{-\frac{816}{25}}{-32}+25^{2}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Express \frac{-\frac{816}{25}}{-32} as a single fraction.

$$\frac{-816}{25\left(-32\right)}+25^{2}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Multiply 25 and -32 to get -800.

$$\frac{-816}{-800}+25^{2}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Reduce the fraction \frac{-816}{-800} to lowest terms by extracting and canceling out -16.

$$\frac{51}{50}+25^{2}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Calculate 25 to the power of 2 and get 625.

$$\frac{51}{50}+625+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Convert 625 to fraction \frac{31250}{50}.

$$\frac{51}{50}+\frac{31250}{50}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Since \frac{51}{50} and \frac{31250}{50} have the same denominator, add them by adding their numerators.

$$\frac{51+31250}{50}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Add 51 and 31250 to get 31301.

$$\frac{31301}{50}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

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

$$\frac{31301}{50}+\left(\frac{3}{6}+\frac{4}{6}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

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

$$\frac{31301}{50}+\left(\frac{3+4}{6}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Add 3 and 4 to get 7.

$$\frac{31301}{50}+\left(\frac{7}{6}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Least common multiple of 6 and 4 is 12. Convert \frac{7}{6} and \frac{3}{4} to fractions with denominator 12.

$$\frac{31301}{50}+\left(\frac{14}{12}-\frac{9}{12}-\frac{11}{12}\right)\times 24$$

Since \frac{14}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{31301}{50}+\left(\frac{14-9}{12}-\frac{11}{12}\right)\times 24$$

Subtract 9 from 14 to get 5.

$$\frac{31301}{50}+\left(\frac{5}{12}-\frac{11}{12}\right)\times 24$$

Since \frac{5}{12} and \frac{11}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{31301}{50}+\frac{5-11}{12}\times 24$$

Subtract 11 from 5 to get -6.

$$\frac{31301}{50}+\frac{-6}{12}\times 24$$

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

$$\frac{31301}{50}-\frac{1}{2}\times 24$$

Express -\frac{1}{2}\times 24 as a single fraction.

$$\frac{31301}{50}+\frac{-24}{2}$$

Divide -24 by 2 to get -12.

$$\frac{31301}{50}-12$$

Convert 12 to fraction \frac{600}{50}.

$$\frac{31301}{50}-\frac{600}{50}$$

Since \frac{31301}{50} and \frac{600}{50} have the same denominator, subtract them by subtracting their numerators.

$$\frac{31301-600}{50}$$

Subtract 600 from 31301 to get 30701.

$$\frac{30701}{50}$$

Factor

$$\frac{11 \cdot 2791}{2 \cdot 5 ^ {2}} = 614\frac{1}{50} = 614.02$$