Solve 12/3-11/4/2*frac{5/6}{frac{2}{3}+frac{3}{8}}

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

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

Solution Steps

Multiply 1 and 3 to get 3.

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

Add 3 and 2 to get 5.

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

Multiply 1 and 4 to get 4.

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

Add 4 and 1 to get 5.

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

Least common multiple of 3 and 4 is 12. Convert \frac{5}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{\frac{20}{12}-\frac{15}{12}}{2}\times \frac{\frac{5}{6}}{\frac{2}{3}+\frac{3}{8}}$$

Since \frac{20}{12} and \frac{15}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{20-15}{12}}{2}\times \frac{\frac{5}{6}}{\frac{2}{3}+\frac{3}{8}}$$

Subtract 15 from 20 to get 5.

$$\frac{\frac{5}{12}}{2}\times \frac{\frac{5}{6}}{\frac{2}{3}+\frac{3}{8}}$$

Express \frac{\frac{5}{12}}{2} as a single fraction.

$$\frac{5}{12\times 2}\times \frac{\frac{5}{6}}{\frac{2}{3}+\frac{3}{8}}$$

Multiply 12 and 2 to get 24.

$$\frac{5}{24}\times \frac{\frac{5}{6}}{\frac{2}{3}+\frac{3}{8}}$$

Least common multiple of 3 and 8 is 24. Convert \frac{2}{3} and \frac{3}{8} to fractions with denominator 24.

$$\frac{5}{24}\times \frac{\frac{5}{6}}{\frac{16}{24}+\frac{9}{24}}$$

Since \frac{16}{24} and \frac{9}{24} have the same denominator, add them by adding their numerators.

$$\frac{5}{24}\times \frac{\frac{5}{6}}{\frac{16+9}{24}}$$

Add 16 and 9 to get 25.

$$\frac{5}{24}\times \frac{\frac{5}{6}}{\frac{25}{24}}$$

Divide \frac{5}{6} by \frac{25}{24} by multiplying \frac{5}{6} by the reciprocal of \frac{25}{24}.

$$\frac{5}{24}\times \frac{5}{6}\times \frac{24}{25}$$

Multiply \frac{5}{6} times \frac{24}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{24}\times \frac{5\times 24}{6\times 25}$$

Do the multiplications in the fraction \frac{5\times 24}{6\times 25}.

$$\frac{5}{24}\times \frac{120}{150}$$

Reduce the fraction \frac{120}{150} to lowest terms by extracting and canceling out 30.

$$\frac{5}{24}\times \frac{4}{5}$$

Multiply \frac{5}{24} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 4}{24\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{4}{24}$$

Reduce the fraction \frac{4}{24} to lowest terms by extracting and canceling out 4.

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$