Solve (4/3-1/6)-[-(1/7+2/6)+frac{5}{4}*frac{1}{9}]

$$( \frac { 4 } { 3 } - \frac { 1 } { 6 } ) - [ - ( \frac { 1 } { 7 } + \frac { 2 } { 6 } ) + \frac { 5 } { 4 } \times \frac { 1 } { 9 } ]$$

Evaluate

$$\frac{379}{252}\approx 1.503968254$$

Solution Steps

Least common multiple of 3 and 6 is 6. Convert \frac{4}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{8}{6}-\frac{1}{6}-\left(-\left(\frac{1}{7}+\frac{2}{6}\right)+\frac{5}{4}\times \frac{1}{9}\right)$$

Since \frac{8}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-1}{6}-\left(-\left(\frac{1}{7}+\frac{2}{6}\right)+\frac{5}{4}\times \frac{1}{9}\right)$$

Subtract 1 from 8 to get 7.

$$\frac{7}{6}-\left(-\left(\frac{1}{7}+\frac{2}{6}\right)+\frac{5}{4}\times \frac{1}{9}\right)$$

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

$$\frac{7}{6}-\left(-\left(\frac{1}{7}+\frac{1}{3}\right)+\frac{5}{4}\times \frac{1}{9}\right)$$

Least common multiple of 7 and 3 is 21. Convert \frac{1}{7} and \frac{1}{3} to fractions with denominator 21.

$$\frac{7}{6}-\left(-\left(\frac{3}{21}+\frac{7}{21}\right)+\frac{5}{4}\times \frac{1}{9}\right)$$

Since \frac{3}{21} and \frac{7}{21} have the same denominator, add them by adding their numerators.

$$\frac{7}{6}-\left(-\frac{3+7}{21}+\frac{5}{4}\times \frac{1}{9}\right)$$

Add 3 and 7 to get 10.

$$\frac{7}{6}-\left(-\frac{10}{21}+\frac{5}{4}\times \frac{1}{9}\right)$$

Multiply \frac{5}{4} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{6}-\left(-\frac{10}{21}+\frac{5\times 1}{4\times 9}\right)$$

Do the multiplications in the fraction \frac{5\times 1}{4\times 9}.

$$\frac{7}{6}-\left(-\frac{10}{21}+\frac{5}{36}\right)$$

Least common multiple of 21 and 36 is 252. Convert -\frac{10}{21} and \frac{5}{36} to fractions with denominator 252.

$$\frac{7}{6}-\left(-\frac{120}{252}+\frac{35}{252}\right)$$

Since -\frac{120}{252} and \frac{35}{252} have the same denominator, add them by adding their numerators.

$$\frac{7}{6}-\frac{-120+35}{252}$$

Add -120 and 35 to get -85.

$$\frac{7}{6}-\left(-\frac{85}{252}\right)$$

The opposite of -\frac{85}{252} is \frac{85}{252}.

$$\frac{7}{6}+\frac{85}{252}$$

Least common multiple of 6 and 252 is 252. Convert \frac{7}{6} and \frac{85}{252} to fractions with denominator 252.

$$\frac{294}{252}+\frac{85}{252}$$

Since \frac{294}{252} and \frac{85}{252} have the same denominator, add them by adding their numerators.

$$\frac{294+85}{252}$$

Add 294 and 85 to get 379.

$$\frac{379}{252}$$

Factor

$$\frac{379}{2 ^ {2} \cdot 3 ^ {2} \cdot 7} = 1\frac{127}{252} = 1.503968253968254$$