Solve (-81)div21/4*4/9*(-3)+|-21/2|+(-37)-|-27|-|-(+71/2)|

$$( - 81 ) \div 2 \frac { 1 } { 4 } \times \frac { 4 } { 9 } \times ( - 3 ) + | - 2 \frac { 1 } { 2 } | + ( - 37 ) - | - 27 | - | - ( + 7 \frac { 1 } { 2 } ) |$$

Evaluate

$$-21$$

Solution Steps

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

$$\frac{-81\times 4}{2\times 4+1}\times \frac{4}{9}\left(-3\right)+|-\frac{2\times 2+1}{2}|-37-|-27|-|-\frac{7\times 2+1}{2}|$$

Multiply -81 and 4 to get -324.

$$\frac{-324}{2\times 4+1}\times \frac{4}{9}\left(-3\right)+|-\frac{2\times 2+1}{2}|-37-|-27|-|-\frac{7\times 2+1}{2}|$$

Multiply 2 and 4 to get 8.

$$\frac{-324}{8+1}\times \frac{4}{9}\left(-3\right)+|-\frac{2\times 2+1}{2}|-37-|-27|-|-\frac{7\times 2+1}{2}|$$

Add 8 and 1 to get 9.

$$\frac{-324}{9}\times \frac{4}{9}\left(-3\right)+|-\frac{2\times 2+1}{2}|-37-|-27|-|-\frac{7\times 2+1}{2}|$$

Divide -324 by 9 to get -36.

$$-36\times \frac{4}{9}\left(-3\right)+|-\frac{2\times 2+1}{2}|-37-|-27|-|-\frac{7\times 2+1}{2}|$$

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

$$\frac{-36\times 4}{9}\left(-3\right)+|-\frac{2\times 2+1}{2}|-37-|-27|-|-\frac{7\times 2+1}{2}|$$

Multiply -36 and 4 to get -144.

$$\frac{-144}{9}\left(-3\right)+|-\frac{2\times 2+1}{2}|-37-|-27|-|-\frac{7\times 2+1}{2}|$$

Divide -144 by 9 to get -16.

$$-16\left(-3\right)+|-\frac{2\times 2+1}{2}|-37-|-27|-|-\frac{7\times 2+1}{2}|$$

Multiply -16 and -3 to get 48.

$$48+|-\frac{2\times 2+1}{2}|-37-|-27|-|-\frac{7\times 2+1}{2}|$$

Multiply 2 and 2 to get 4.

$$48+|-\frac{4+1}{2}|-37-|-27|-|-\frac{7\times 2+1}{2}|$$

Add 4 and 1 to get 5.

$$48+|-\frac{5}{2}|-37-|-27|-|-\frac{7\times 2+1}{2}|$$

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}.

$$48+\frac{5}{2}-37-|-27|-|-\frac{7\times 2+1}{2}|$$

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

$$\frac{96}{2}+\frac{5}{2}-37-|-27|-|-\frac{7\times 2+1}{2}|$$

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

$$\frac{96+5}{2}-37-|-27|-|-\frac{7\times 2+1}{2}|$$

Add 96 and 5 to get 101.

$$\frac{101}{2}-37-|-27|-|-\frac{7\times 2+1}{2}|$$

Convert 37 to fraction \frac{74}{2}.

$$\frac{101}{2}-\frac{74}{2}-|-27|-|-\frac{7\times 2+1}{2}|$$

Since \frac{101}{2} and \frac{74}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{101-74}{2}-|-27|-|-\frac{7\times 2+1}{2}|$$

Subtract 74 from 101 to get 27.

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

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -27 is 27.

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

Convert 27 to fraction \frac{54}{2}.

$$\frac{27}{2}-\frac{54}{2}-|-\frac{7\times 2+1}{2}|$$

Since \frac{27}{2} and \frac{54}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-54}{2}-|-\frac{7\times 2+1}{2}|$$

Subtract 54 from 27 to get -27.

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

Multiply 7 and 2 to get 14.

$$-\frac{27}{2}-|-\frac{14+1}{2}|$$

Add 14 and 1 to get 15.

$$-\frac{27}{2}-|-\frac{15}{2}|$$

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}.

$$-\frac{27}{2}-\frac{15}{2}$$

Since -\frac{27}{2} and \frac{15}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-27-15}{2}$$

Subtract 15 from -27 to get -42.

$$\frac{-42}{2}$$

Divide -42 by 2 to get -21.

$$-21$$

Factor

$$-21$$