Solve {l}{1/4+4*(1/4+4*(1/4+4*(1/4+4*(frac{1}{4}-frac{1}{3}))))}{-2*(frac{1}{2}-2*(frac{1}{2}-frac{1}{3})))]*text{Hamepere}4.A}

$$\left. \begin{array} { l } { \frac { 1 } { 4 } + 4 \cdot ( \frac { 1 } { 4 } + 4 \cdot ( \frac { 1 } { 4 } + 4 \cdot ( \frac { 1 } { 4 } + 4 \cdot ( \frac { 1 } { 4 } - \frac { 1 } { 3 } ) ) ) ) } \\ { - 2 \cdot ( \frac { 1 } { 2 } - 2 \cdot ( \frac { 1 } { 2 } - \frac { 1 } { 3 } ) ) ) ] \cdot \text { Hamepere } 4 . A } \end{array} \right.$$

Evaluate

$$-\frac{5}{12}\approx -0.416666667$$

Solution Steps

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{1}{3} to fractions with denominator 12.

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

Since \frac{3}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 3 to get -1.

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

Express 4\left(-\frac{1}{12}\right) as a single fraction.

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

Multiply 4 and -1 to get -4.

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

Reduce the fraction \frac{-4}{12} to lowest terms by extracting and canceling out 4.

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

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{1}{3} to fractions with denominator 12.

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

Since \frac{3}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 3 to get -1.

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

Express 4\left(-\frac{1}{12}\right) as a single fraction.

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

Multiply 4 and -1 to get -4.

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

Reduce the fraction \frac{-4}{12} to lowest terms by extracting and canceling out 4.

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

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{1}{3} to fractions with denominator 12.

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

Since \frac{3}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 3 to get -1.

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

Express 4\left(-\frac{1}{12}\right) as a single fraction.

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

Multiply 4 and -1 to get -4.

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

Reduce the fraction \frac{-4}{12} to lowest terms by extracting and canceling out 4.

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

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{1}{3} to fractions with denominator 12.

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

Since \frac{3}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 3 to get -1.

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

Express 4\left(-\frac{1}{12}\right) as a single fraction.

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

Multiply 4 and -1 to get -4.

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

Reduce the fraction \frac{-4}{12} to lowest terms by extracting and canceling out 4.

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

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{1}{3} to fractions with denominator 12.

$$\frac{3}{12}-\frac{4}{12}-2\left(\frac{1}{2}-2\left(\frac{1}{2}-\frac{1}{3}\right)\right)$$

Since \frac{3}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-4}{12}-2\left(\frac{1}{2}-2\left(\frac{1}{2}-\frac{1}{3}\right)\right)$$

Subtract 4 from 3 to get -1.

$$-\frac{1}{12}-2\left(\frac{1}{2}-2\left(\frac{1}{2}-\frac{1}{3}\right)\right)$$

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

$$-\frac{1}{12}-2\left(\frac{1}{2}-2\left(\frac{3}{6}-\frac{2}{6}\right)\right)$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{12}-2\left(\frac{1}{2}-2\times \frac{3-2}{6}\right)$$

Subtract 2 from 3 to get 1.

$$-\frac{1}{12}-2\left(\frac{1}{2}-2\times \frac{1}{6}\right)$$

Multiply 2 and \frac{1}{6} to get \frac{2}{6}.

$$-\frac{1}{12}-2\left(\frac{1}{2}-\frac{2}{6}\right)$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{12}-2\left(\frac{1}{2}-\frac{1}{3}\right)$$

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

$$-\frac{1}{12}-2\left(\frac{3}{6}-\frac{2}{6}\right)$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{12}-2\times \frac{3-2}{6}$$

Subtract 2 from 3 to get 1.

$$-\frac{1}{12}-2\times \frac{1}{6}$$

Multiply 2 and \frac{1}{6} to get \frac{2}{6}.

$$-\frac{1}{12}-\frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{12}-\frac{1}{3}$$

Least common multiple of 12 and 3 is 12. Convert -\frac{1}{12} and \frac{1}{3} to fractions with denominator 12.

$$-\frac{1}{12}-\frac{4}{12}$$

Since -\frac{1}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-4}{12}$$

Subtract 4 from -1 to get -5.

$$-\frac{5}{12}$$

Factor

$$-\frac{5}{12} = -0.4166666666666667$$