Solve 1/6text{of}(31/2-21/4)+51/8divfrac{3}{16}-frac{1}{2}

$$\frac { 1 } { 6 } \text { of } ( 3 \frac { 1 } { 2 } - 2 \frac { 1 } { 4 } ) + 5 \frac { 1 } { 8 } \div \frac { 3 } { 16 } - \frac { 1 } { 2 }$$

Evaluate

$$\frac{649}{24}\approx 27.041666667$$

Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{1}{6}\left(\frac{6+1}{2}-\frac{2\times 4+1}{4}\right)+\frac{\frac{5\times 8+1}{8}}{\frac{3}{16}}-\frac{1}{2}$$

Add 6 and 1 to get 7.

$$\frac{1}{6}\left(\frac{7}{2}-\frac{2\times 4+1}{4}\right)+\frac{\frac{5\times 8+1}{8}}{\frac{3}{16}}-\frac{1}{2}$$

Multiply 2 and 4 to get 8.

$$\frac{1}{6}\left(\frac{7}{2}-\frac{8+1}{4}\right)+\frac{\frac{5\times 8+1}{8}}{\frac{3}{16}}-\frac{1}{2}$$

Add 8 and 1 to get 9.

$$\frac{1}{6}\left(\frac{7}{2}-\frac{9}{4}\right)+\frac{\frac{5\times 8+1}{8}}{\frac{3}{16}}-\frac{1}{2}$$

Least common multiple of 2 and 4 is 4. Convert \frac{7}{2} and \frac{9}{4} to fractions with denominator 4.

$$\frac{1}{6}\left(\frac{14}{4}-\frac{9}{4}\right)+\frac{\frac{5\times 8+1}{8}}{\frac{3}{16}}-\frac{1}{2}$$

Since \frac{14}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}\times \frac{14-9}{4}+\frac{\frac{5\times 8+1}{8}}{\frac{3}{16}}-\frac{1}{2}$$

Subtract 9 from 14 to get 5.

$$\frac{1}{6}\times \frac{5}{4}+\frac{\frac{5\times 8+1}{8}}{\frac{3}{16}}-\frac{1}{2}$$

Multiply \frac{1}{6} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 5}{6\times 4}+\frac{\frac{5\times 8+1}{8}}{\frac{3}{16}}-\frac{1}{2}$$

Do the multiplications in the fraction \frac{1\times 5}{6\times 4}.

$$\frac{5}{24}+\frac{\frac{5\times 8+1}{8}}{\frac{3}{16}}-\frac{1}{2}$$

Divide \frac{5\times 8+1}{8} by \frac{3}{16} by multiplying \frac{5\times 8+1}{8} by the reciprocal of \frac{3}{16}.

$$\frac{5}{24}+\frac{\left(5\times 8+1\right)\times 16}{8\times 3}-\frac{1}{2}$$

Cancel out 8 in both numerator and denominator.

$$\frac{5}{24}+\frac{2\left(1+5\times 8\right)}{3}-\frac{1}{2}$$

Multiply 5 and 8 to get 40.

$$\frac{5}{24}+\frac{2\left(1+40\right)}{3}-\frac{1}{2}$$

Add 1 and 40 to get 41.

$$\frac{5}{24}+\frac{2\times 41}{3}-\frac{1}{2}$$

Multiply 2 and 41 to get 82.

$$\frac{5}{24}+\frac{82}{3}-\frac{1}{2}$$

Least common multiple of 24 and 3 is 24. Convert \frac{5}{24} and \frac{82}{3} to fractions with denominator 24.

$$\frac{5}{24}+\frac{656}{24}-\frac{1}{2}$$

Since \frac{5}{24} and \frac{656}{24} have the same denominator, add them by adding their numerators.

$$\frac{5+656}{24}-\frac{1}{2}$$

Add 5 and 656 to get 661.

$$\frac{661}{24}-\frac{1}{2}$$

Least common multiple of 24 and 2 is 24. Convert \frac{661}{24} and \frac{1}{2} to fractions with denominator 24.

$$\frac{661}{24}-\frac{12}{24}$$

Since \frac{661}{24} and \frac{12}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{661-12}{24}$$

Subtract 12 from 661 to get 649.

$$\frac{649}{24}$$

Factor

$$\frac{11 \cdot 59}{2 ^ {3} \cdot 3} = 27\frac{1}{24} = 27.041666666666668$$