Solve 5-{-1/5+5/4|-3+7/6-(4/5-1)|-frac{1}{6}}-frac{2}{3}

$$5 - \{ - \frac { 1 } { 5 } + \frac { 5 } { 4 } | - 3 + \frac { 7 } { 6 } - ( \frac { 4 } { 5 } - 1 ) | - \frac { 1 } { 6 } \} - \frac { 2 } { 3 }$$

Evaluate

$$\frac{319}{120}\approx 2.658333333$$

Solution Steps

Convert -3 to fraction -\frac{18}{6}.

$$5-\left(-\frac{1}{5}+\frac{5}{4}|-\frac{18}{6}+\frac{7}{6}-\left(\frac{4}{5}-1\right)|-\frac{1}{6}\right)-\frac{2}{3}$$

Since -\frac{18}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$5-\left(-\frac{1}{5}+\frac{5}{4}|\frac{-18+7}{6}-\left(\frac{4}{5}-1\right)|-\frac{1}{6}\right)-\frac{2}{3}$$

Add -18 and 7 to get -11.

$$5-\left(-\frac{1}{5}+\frac{5}{4}|-\frac{11}{6}-\left(\frac{4}{5}-1\right)|-\frac{1}{6}\right)-\frac{2}{3}$$

Convert 1 to fraction \frac{5}{5}.

$$5-\left(-\frac{1}{5}+\frac{5}{4}|-\frac{11}{6}-\left(\frac{4}{5}-\frac{5}{5}\right)|-\frac{1}{6}\right)-\frac{2}{3}$$

Since \frac{4}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$5-\left(-\frac{1}{5}+\frac{5}{4}|-\frac{11}{6}-\frac{4-5}{5}|-\frac{1}{6}\right)-\frac{2}{3}$$

Subtract 5 from 4 to get -1.

$$5-\left(-\frac{1}{5}+\frac{5}{4}|-\frac{11}{6}-\left(-\frac{1}{5}\right)|-\frac{1}{6}\right)-\frac{2}{3}$$

The opposite of -\frac{1}{5} is \frac{1}{5}.

$$5-\left(-\frac{1}{5}+\frac{5}{4}|-\frac{11}{6}+\frac{1}{5}|-\frac{1}{6}\right)-\frac{2}{3}$$

Least common multiple of 6 and 5 is 30. Convert -\frac{11}{6} and \frac{1}{5} to fractions with denominator 30.

$$5-\left(-\frac{1}{5}+\frac{5}{4}|-\frac{55}{30}+\frac{6}{30}|-\frac{1}{6}\right)-\frac{2}{3}$$

Since -\frac{55}{30} and \frac{6}{30} have the same denominator, add them by adding their numerators.

$$5-\left(-\frac{1}{5}+\frac{5}{4}|\frac{-55+6}{30}|-\frac{1}{6}\right)-\frac{2}{3}$$

Add -55 and 6 to get -49.

$$5-\left(-\frac{1}{5}+\frac{5}{4}|-\frac{49}{30}|-\frac{1}{6}\right)-\frac{2}{3}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{49}{30} is \frac{49}{30}.

$$5-\left(-\frac{1}{5}+\frac{5}{4}\times \frac{49}{30}-\frac{1}{6}\right)-\frac{2}{3}$$

Multiply \frac{5}{4} times \frac{49}{30} by multiplying numerator times numerator and denominator times denominator.

$$5-\left(-\frac{1}{5}+\frac{5\times 49}{4\times 30}-\frac{1}{6}\right)-\frac{2}{3}$$

Do the multiplications in the fraction \frac{5\times 49}{4\times 30}.

$$5-\left(-\frac{1}{5}+\frac{245}{120}-\frac{1}{6}\right)-\frac{2}{3}$$

Reduce the fraction \frac{245}{120} to lowest terms by extracting and canceling out 5.

$$5-\left(-\frac{1}{5}+\frac{49}{24}-\frac{1}{6}\right)-\frac{2}{3}$$

Least common multiple of 5 and 24 is 120. Convert -\frac{1}{5} and \frac{49}{24} to fractions with denominator 120.

$$5-\left(-\frac{24}{120}+\frac{245}{120}-\frac{1}{6}\right)-\frac{2}{3}$$

Since -\frac{24}{120} and \frac{245}{120} have the same denominator, add them by adding their numerators.

$$5-\left(\frac{-24+245}{120}-\frac{1}{6}\right)-\frac{2}{3}$$

Add -24 and 245 to get 221.

$$5-\left(\frac{221}{120}-\frac{1}{6}\right)-\frac{2}{3}$$

Least common multiple of 120 and 6 is 120. Convert \frac{221}{120} and \frac{1}{6} to fractions with denominator 120.

$$5-\left(\frac{221}{120}-\frac{20}{120}\right)-\frac{2}{3}$$

Since \frac{221}{120} and \frac{20}{120} have the same denominator, subtract them by subtracting their numerators.

$$5-\frac{221-20}{120}-\frac{2}{3}$$

Subtract 20 from 221 to get 201.

$$5-\frac{201}{120}-\frac{2}{3}$$

Reduce the fraction \frac{201}{120} to lowest terms by extracting and canceling out 3.

$$5-\frac{67}{40}-\frac{2}{3}$$

Convert 5 to fraction \frac{200}{40}.

$$\frac{200}{40}-\frac{67}{40}-\frac{2}{3}$$

Since \frac{200}{40} and \frac{67}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{200-67}{40}-\frac{2}{3}$$

Subtract 67 from 200 to get 133.

$$\frac{133}{40}-\frac{2}{3}$$

Least common multiple of 40 and 3 is 120. Convert \frac{133}{40} and \frac{2}{3} to fractions with denominator 120.

$$\frac{399}{120}-\frac{80}{120}$$

Since \frac{399}{120} and \frac{80}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{399-80}{120}$$

Subtract 80 from 399 to get 319.

$$\frac{319}{120}$$

Factor

$$\frac{11 \cdot 29}{2 ^ {3} \cdot 3 \cdot 5} = 2\frac{79}{120} = 2.658333333333333$$