Solve (-81)div21/4*4/9*(-3)+|-21/2|+(-3.7)-|-2.7|-|-(+71/2)|

$$( - 81 ) \div 2 \frac { 1 } { 4 } \times \frac { 4 } { 9 } \times ( - 3 ) + | - 2 \frac { 1 } { 2 } | + ( - 3.7 ) - | - 2.7 | - | - ( + 7 \frac { 1 } { 2 } ) |$$

Evaluate

$$36.6$$

Solution Steps

Divide -81 by \frac{2\times 4+1}{4} by multiplying -81 by the reciprocal of \frac{2\times 4+1}{4}.

$$\frac{-81\times 4}{2\times 4+1}\times \frac{4}{9}\left(-3\right)+|-\frac{2\times 2+1}{2}|-3.7-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Multiply -81 and 4 to get -324.

$$\frac{-324}{2\times 4+1}\times \frac{4}{9}\left(-3\right)+|-\frac{2\times 2+1}{2}|-3.7-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Multiply 2 and 4 to get 8.

$$\frac{-324}{8+1}\times \frac{4}{9}\left(-3\right)+|-\frac{2\times 2+1}{2}|-3.7-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Add 8 and 1 to get 9.

$$\frac{-324}{9}\times \frac{4}{9}\left(-3\right)+|-\frac{2\times 2+1}{2}|-3.7-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Divide -324 by 9 to get -36.

$$-36\times \frac{4}{9}\left(-3\right)+|-\frac{2\times 2+1}{2}|-3.7-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Express -36\times \frac{4}{9} as a single fraction.

$$\frac{-36\times 4}{9}\left(-3\right)+|-\frac{2\times 2+1}{2}|-3.7-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Multiply -36 and 4 to get -144.

$$\frac{-144}{9}\left(-3\right)+|-\frac{2\times 2+1}{2}|-3.7-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Divide -144 by 9 to get -16.

$$-16\left(-3\right)+|-\frac{2\times 2+1}{2}|-3.7-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Multiply -16 and -3 to get 48.

$$48+|-\frac{2\times 2+1}{2}|-3.7-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Multiply 2 and 2 to get 4.

$$48+|-\frac{4+1}{2}|-3.7-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Add 4 and 1 to get 5.

$$48+|-\frac{5}{2}|-3.7-|-2.7|-|-\frac{7\times 2+1}{2}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{5}{2} is \frac{5}{2}.

$$48+\frac{5}{2}-3.7-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Convert 48 to fraction \frac{96}{2}.

$$\frac{96}{2}+\frac{5}{2}-3.7-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Since \frac{96}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$\frac{96+5}{2}-3.7-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Add 96 and 5 to get 101.

$$\frac{101}{2}-3.7-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Convert decimal number 3.7 to fraction \frac{37}{10}.

$$\frac{101}{2}-\frac{37}{10}-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Least common multiple of 2 and 10 is 10. Convert \frac{101}{2} and \frac{37}{10} to fractions with denominator 10.

$$\frac{505}{10}-\frac{37}{10}-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Since \frac{505}{10} and \frac{37}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{505-37}{10}-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Subtract 37 from 505 to get 468.

$$\frac{468}{10}-|-2.7|-|-\frac{7\times 2+1}{2}|$$

Reduce the fraction \frac{468}{10} to lowest terms by extracting and canceling out 2.

$$\frac{234}{5}-|-2.7|-|-\frac{7\times 2+1}{2}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2.7 is 2.7.

$$\frac{234}{5}-2.7-|-\frac{7\times 2+1}{2}|$$

Convert decimal number 2.7 to fraction \frac{27}{10}.

$$\frac{234}{5}-\frac{27}{10}-|-\frac{7\times 2+1}{2}|$$

Least common multiple of 5 and 10 is 10. Convert \frac{234}{5} and \frac{27}{10} to fractions with denominator 10.

$$\frac{468}{10}-\frac{27}{10}-|-\frac{7\times 2+1}{2}|$$

Since \frac{468}{10} and \frac{27}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{468-27}{10}-|-\frac{7\times 2+1}{2}|$$

Subtract 27 from 468 to get 441.

$$\frac{441}{10}-|-\frac{7\times 2+1}{2}|$$

Multiply 7 and 2 to get 14.

$$\frac{441}{10}-|-\frac{14+1}{2}|$$

Add 14 and 1 to get 15.

$$\frac{441}{10}-|-\frac{15}{2}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{15}{2} is \frac{15}{2}.

$$\frac{441}{10}-\frac{15}{2}$$

Least common multiple of 10 and 2 is 10. Convert \frac{441}{10} and \frac{15}{2} to fractions with denominator 10.

$$\frac{441}{10}-\frac{75}{10}$$

Since \frac{441}{10} and \frac{75}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{441-75}{10}$$

Subtract 75 from 441 to get 366.

$$\frac{366}{10}$$

Reduce the fraction \frac{366}{10} to lowest terms by extracting and canceling out 2.

$$\frac{183}{5}$$

Factor

$$\frac{3 \cdot 61}{5} = 36\frac{3}{5} = 36.6$$