Solve 1=21/4*4/9*(-3)+|-21/2|+(-37)-|-27|-|-(+71/2)|

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

Verify

Solution Steps

Multiply both sides of the equation by 36, the least common multiple of 4,9.

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

Multiply 2 and 4 to get 8.

$$36=36\left(\frac{8+1}{4}\times \frac{4}{9}\left(-3\right)+|-\frac{2\times 2+1}{2}|-37-|-27|\right)-36|-\frac{7\times 2+1}{2}|$$

Add 8 and 1 to get 9.

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

Cancel out \frac{9}{4} and its reciprocal \frac{4}{9}.

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

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

$$36=36\left(-3+|-\frac{5}{2}|-37-|-27|\right)-36|-\frac{7\times 2+1}{2}|$$

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}.

$$36=36\left(-3+\frac{5}{2}-37-|-27|\right)-36|-\frac{7\times 2+1}{2}|$$

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

$$36=36\left(-\frac{6}{2}+\frac{5}{2}-37-|-27|\right)-36|-\frac{7\times 2+1}{2}|$$

Since -\frac{6}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$36=36\left(\frac{-6+5}{2}-37-|-27|\right)-36|-\frac{7\times 2+1}{2}|$$

Add -6 and 5 to get -1.

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

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

$$36=36\left(-\frac{1}{2}-\frac{74}{2}-|-27|\right)-36|-\frac{7\times 2+1}{2}|$$

Since -\frac{1}{2} and \frac{74}{2} have the same denominator, subtract them by subtracting their numerators.

$$36=36\left(\frac{-1-74}{2}-|-27|\right)-36|-\frac{7\times 2+1}{2}|$$

Subtract 74 from -1 to get -75.

$$36=36\left(-\frac{75}{2}-|-27|\right)-36|-\frac{7\times 2+1}{2}|$$

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.

$$36=36\left(-\frac{75}{2}-27\right)-36|-\frac{7\times 2+1}{2}|$$

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

$$36=36\left(-\frac{75}{2}-\frac{54}{2}\right)-36|-\frac{7\times 2+1}{2}|$$

Since -\frac{75}{2} and \frac{54}{2} have the same denominator, subtract them by subtracting their numerators.

$$36=36\times \frac{-75-54}{2}-36|-\frac{7\times 2+1}{2}|$$

Subtract 54 from -75 to get -129.

$$36=36\left(-\frac{129}{2}\right)-36|-\frac{7\times 2+1}{2}|$$

Express 36\left(-\frac{129}{2}\right) as a single fraction.

$$36=\frac{36\left(-129\right)}{2}-36|-\frac{7\times 2+1}{2}|$$

Multiply 36 and -129 to get -4644.

$$36=\frac{-4644}{2}-36|-\frac{7\times 2+1}{2}|$$

Divide -4644 by 2 to get -2322.

$$36=-2322-36|-\frac{7\times 2+1}{2}|$$

Multiply 7 and 2 to get 14.

$$36=-2322-36|-\frac{14+1}{2}|$$

Add 14 and 1 to get 15.

$$36=-2322-36|-\frac{15}{2}|$$

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}.

$$36=-2322-36\times \frac{15}{2}$$

Express 36\times \frac{15}{2} as a single fraction.

$$36=-2322-\frac{36\times 15}{2}$$

Multiply 36 and 15 to get 540.

$$36=-2322-\frac{540}{2}$$

Divide 540 by 2 to get 270.

$$36=-2322-270$$

Subtract 270 from -2322 to get -2592.

$$36=-2592$$

Compare 36 and -2592.

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