Solve -3216/25div(-8*4)+2.5^2+(1/2+2/3-3/4-frac{11}{12})*24

$$- 32 \frac { 16 } { 25 } \div ( - 8 \times 4 ) + 2.5 ^ { 2 } + ( \frac { 1 } { 2 } + \frac { 2 } { 3 } - \frac { 3 } { 4 } - \frac { 11 } { 12 } ) \times 24$$

Evaluate

$$-4.73$$

Solution Steps

Multiply 32 and 25 to get 800.

$$\frac{-\frac{800+16}{25}}{-8\times 4}+2.5^{2}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Add 800 and 16 to get 816.

$$\frac{-\frac{816}{25}}{-8\times 4}+2.5^{2}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Multiply -8 and 4 to get -32.

$$\frac{-\frac{816}{25}}{-32}+2.5^{2}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

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

$$\frac{-816}{25\left(-32\right)}+2.5^{2}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Multiply 25 and -32 to get -800.

$$\frac{-816}{-800}+2.5^{2}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

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

$$\frac{51}{50}+2.5^{2}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Calculate 2.5 to the power of 2 and get 6.25.

$$\frac{51}{50}+6.25+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Convert decimal number 6.25 to fraction \frac{625}{100}. Reduce the fraction \frac{625}{100} to lowest terms by extracting and canceling out 25.

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

Least common multiple of 50 and 4 is 100. Convert \frac{51}{50} and \frac{25}{4} to fractions with denominator 100.

$$\frac{102}{100}+\frac{625}{100}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Since \frac{102}{100} and \frac{625}{100} have the same denominator, add them by adding their numerators.

$$\frac{102+625}{100}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Add 102 and 625 to get 727.

$$\frac{727}{100}+\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

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

$$\frac{727}{100}+\left(\frac{3}{6}+\frac{4}{6}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

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

$$\frac{727}{100}+\left(\frac{3+4}{6}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

Add 3 and 4 to get 7.

$$\frac{727}{100}+\left(\frac{7}{6}-\frac{3}{4}-\frac{11}{12}\right)\times 24$$

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

$$\frac{727}{100}+\left(\frac{14}{12}-\frac{9}{12}-\frac{11}{12}\right)\times 24$$

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

$$\frac{727}{100}+\left(\frac{14-9}{12}-\frac{11}{12}\right)\times 24$$

Subtract 9 from 14 to get 5.

$$\frac{727}{100}+\left(\frac{5}{12}-\frac{11}{12}\right)\times 24$$

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

$$\frac{727}{100}+\frac{5-11}{12}\times 24$$

Subtract 11 from 5 to get -6.

$$\frac{727}{100}+\frac{-6}{12}\times 24$$

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

$$\frac{727}{100}-\frac{1}{2}\times 24$$

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

$$\frac{727}{100}+\frac{-24}{2}$$

Divide -24 by 2 to get -12.

$$\frac{727}{100}-12$$

Convert 12 to fraction \frac{1200}{100}.

$$\frac{727}{100}-\frac{1200}{100}$$

Since \frac{727}{100} and \frac{1200}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{727-1200}{100}$$

Subtract 1200 from 727 to get -473.

$$-\frac{473}{100}$$

Factor

$$-4.73$$