Solve ((1/4-1-1/2+3)-(81/4-27-9/2+9))-2(1-3)

$$(( \frac{ 1 }{ 4 } -1- \frac{ 1 }{ 2 } +3)-( \frac{ 81 }{ 4 } -27- \frac{ 9 }{ 2 } +9))-2(1-3)$$

Evaluate

$$8$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

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

Since \frac{1}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 1 to get -3.

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

Least common multiple of 4 and 2 is 4. Convert -\frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

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

Since -\frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from -3 to get -5.

$$-\frac{5}{4}+3-\left(\frac{81}{4}-27-\frac{9}{2}+9\right)-2\left(1-3\right)$$

Convert 3 to fraction \frac{12}{4}.

$$-\frac{5}{4}+\frac{12}{4}-\left(\frac{81}{4}-27-\frac{9}{2}+9\right)-2\left(1-3\right)$$

Since -\frac{5}{4} and \frac{12}{4} have the same denominator, add them by adding their numerators.

$$\frac{-5+12}{4}-\left(\frac{81}{4}-27-\frac{9}{2}+9\right)-2\left(1-3\right)$$

Add -5 and 12 to get 7.

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

Convert 27 to fraction \frac{108}{4}.

$$\frac{7}{4}-\left(\frac{81}{4}-\frac{108}{4}-\frac{9}{2}+9\right)-2\left(1-3\right)$$

Since \frac{81}{4} and \frac{108}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{4}-\left(\frac{81-108}{4}-\frac{9}{2}+9\right)-2\left(1-3\right)$$

Subtract 108 from 81 to get -27.

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

Least common multiple of 4 and 2 is 4. Convert -\frac{27}{4} and \frac{9}{2} to fractions with denominator 4.

$$\frac{7}{4}-\left(-\frac{27}{4}-\frac{18}{4}+9\right)-2\left(1-3\right)$$

Since -\frac{27}{4} and \frac{18}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{4}-\left(\frac{-27-18}{4}+9\right)-2\left(1-3\right)$$

Subtract 18 from -27 to get -45.

$$\frac{7}{4}-\left(-\frac{45}{4}+9\right)-2\left(1-3\right)$$

Convert 9 to fraction \frac{36}{4}.

$$\frac{7}{4}-\left(-\frac{45}{4}+\frac{36}{4}\right)-2\left(1-3\right)$$

Since -\frac{45}{4} and \frac{36}{4} have the same denominator, add them by adding their numerators.

$$\frac{7}{4}-\frac{-45+36}{4}-2\left(1-3\right)$$

Add -45 and 36 to get -9.

$$\frac{7}{4}-\left(-\frac{9}{4}\right)-2\left(1-3\right)$$

The opposite of -\frac{9}{4} is \frac{9}{4}.

$$\frac{7}{4}+\frac{9}{4}-2\left(1-3\right)$$

Since \frac{7}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

$$\frac{7+9}{4}-2\left(1-3\right)$$

Add 7 and 9 to get 16.

$$\frac{16}{4}-2\left(1-3\right)$$

Divide 16 by 4 to get 4.

$$4-2\left(1-3\right)$$

Subtract 3 from 1 to get -2.

$$4-2\left(-2\right)$$

Multiply 2 and -2 to get -4.

$$4-\left(-4\right)$$

The opposite of -4 is 4.

$$4+4$$

Add 4 and 4 to get 8.

$$8$$

Factor

$$2^{3}$$