Solve 2+7(1+1/6)(2+2/3)-1/8

$$2 + 7 ( 1 + \frac { 1 } { 6 } ) ( 2 + \frac { 2 } { 3 } ) - \frac { 1 } { 8 }$$

Evaluate

$$\frac{1703}{72}\approx 23.652777778$$

Solution Steps

Convert 1 to fraction \frac{6}{6}.

$$2+7\left(\frac{6}{6}+\frac{1}{6}\right)\left(2+\frac{2}{3}\right)-\frac{1}{8}$$

Since \frac{6}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$2+7\times \frac{6+1}{6}\left(2+\frac{2}{3}\right)-\frac{1}{8}$$

Add 6 and 1 to get 7.

$$2+7\times \frac{7}{6}\left(2+\frac{2}{3}\right)-\frac{1}{8}$$

Express 7\times \frac{7}{6} as a single fraction.

$$2+\frac{7\times 7}{6}\left(2+\frac{2}{3}\right)-\frac{1}{8}$$

Multiply 7 and 7 to get 49.

$$2+\frac{49}{6}\left(2+\frac{2}{3}\right)-\frac{1}{8}$$

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

$$2+\frac{49}{6}\left(\frac{6}{3}+\frac{2}{3}\right)-\frac{1}{8}$$

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

$$2+\frac{49}{6}\times \frac{6+2}{3}-\frac{1}{8}$$

Add 6 and 2 to get 8.

$$2+\frac{49}{6}\times \frac{8}{3}-\frac{1}{8}$$

Multiply \frac{49}{6} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$2+\frac{49\times 8}{6\times 3}-\frac{1}{8}$$

Do the multiplications in the fraction \frac{49\times 8}{6\times 3}.

$$2+\frac{392}{18}-\frac{1}{8}$$

Reduce the fraction \frac{392}{18} to lowest terms by extracting and canceling out 2.

$$2+\frac{196}{9}-\frac{1}{8}$$

Convert 2 to fraction \frac{18}{9}.

$$\frac{18}{9}+\frac{196}{9}-\frac{1}{8}$$

Since \frac{18}{9} and \frac{196}{9} have the same denominator, add them by adding their numerators.

$$\frac{18+196}{9}-\frac{1}{8}$$

Add 18 and 196 to get 214.

$$\frac{214}{9}-\frac{1}{8}$$

Least common multiple of 9 and 8 is 72. Convert \frac{214}{9} and \frac{1}{8} to fractions with denominator 72.

$$\frac{1712}{72}-\frac{9}{72}$$

Since \frac{1712}{72} and \frac{9}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1712-9}{72}$$

Subtract 9 from 1712 to get 1703.

$$\frac{1703}{72}$$

Factor

$$\frac{13 \cdot 131}{2 ^ {3} \cdot 3 ^ {2}} = 23\frac{47}{72} = 23.65277777777778$$