Solve 2/3text{of}(51/6-43/8)div11/18

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

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Multiply 5 and 6 to get 30.

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

Add 30 and 1 to get 31.

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

Multiply 4 and 8 to get 32.

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

Add 32 and 3 to get 35.

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

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

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

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

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

Subtract 105 from 124 to get 19.

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

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

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

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

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

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

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

Multiply 1 and 18 to get 18.

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

Add 18 and 1 to get 19.

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

Divide \frac{19}{36} by \frac{19}{18} by multiplying \frac{19}{36} by the reciprocal of \frac{19}{18}.

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

Multiply \frac{19}{36} times \frac{18}{19} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 19 in both numerator and denominator.

$$\frac{18}{36}$$

Reduce the fraction \frac{18}{36} to lowest terms by extracting and canceling out 18.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$