Solve 2/3*(51/6-43/8)-11/18

$$\frac { 2 } { 3 } \times ( 5 \frac { 1 } { 6 } - 4 \frac { 3 } { 8 } ) - 1 \frac { 1 } { 18 }$$

Evaluate

$$-\frac{19}{36}\approx -0.527777778$$

Solution Steps

Multiply 5 and 6 to get 30.

$$\frac{2}{3}\left(\frac{30+1}{6}-\frac{4\times 8+3}{8}\right)-\frac{1\times 18+1}{18}$$

Add 30 and 1 to get 31.

$$\frac{2}{3}\left(\frac{31}{6}-\frac{4\times 8+3}{8}\right)-\frac{1\times 18+1}{18}$$

Multiply 4 and 8 to get 32.

$$\frac{2}{3}\left(\frac{31}{6}-\frac{32+3}{8}\right)-\frac{1\times 18+1}{18}$$

Add 32 and 3 to get 35.

$$\frac{2}{3}\left(\frac{31}{6}-\frac{35}{8}\right)-\frac{1\times 18+1}{18}$$

Least common multiple of 6 and 8 is 24. Convert \frac{31}{6} and \frac{35}{8} to fractions with denominator 24.

$$\frac{2}{3}\left(\frac{124}{24}-\frac{105}{24}\right)-\frac{1\times 18+1}{18}$$

Since \frac{124}{24} and \frac{105}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}\times \frac{124-105}{24}-\frac{1\times 18+1}{18}$$

Subtract 105 from 124 to get 19.

$$\frac{2}{3}\times \frac{19}{24}-\frac{1\times 18+1}{18}$$

Multiply \frac{2}{3} times \frac{19}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 19}{3\times 24}-\frac{1\times 18+1}{18}$$

Do the multiplications in the fraction \frac{2\times 19}{3\times 24}.

$$\frac{38}{72}-\frac{1\times 18+1}{18}$$

Reduce the fraction \frac{38}{72} to lowest terms by extracting and canceling out 2.

$$\frac{19}{36}-\frac{1\times 18+1}{18}$$

Multiply 1 and 18 to get 18.

$$\frac{19}{36}-\frac{18+1}{18}$$

Add 18 and 1 to get 19.

$$\frac{19}{36}-\frac{19}{18}$$

Least common multiple of 36 and 18 is 36. Convert \frac{19}{36} and \frac{19}{18} to fractions with denominator 36.

$$\frac{19}{36}-\frac{38}{36}$$

Since \frac{19}{36} and \frac{38}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19-38}{36}$$

Subtract 38 from 19 to get -19.

$$-\frac{19}{36}$$

Factor

$$-\frac{19}{36} = -0.5277777777777778$$