Solve 31/3*2-45/6/4frac{5{5}*2-31/2}

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

Evaluate

$$\frac{11}{39}\approx 0.282051282$$

Solution Steps

Multiply 3 and 3 to get 9.

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

Add 9 and 1 to get 10.

$$\frac{\frac{10}{3}\times 2-\frac{4\times 6+5}{6}}{\frac{4\times 5+5}{5}\times 2-\frac{3\times 2+1}{2}}$$

Express \frac{10}{3}\times 2 as a single fraction.

$$\frac{\frac{10\times 2}{3}-\frac{4\times 6+5}{6}}{\frac{4\times 5+5}{5}\times 2-\frac{3\times 2+1}{2}}$$

Multiply 10 and 2 to get 20.

$$\frac{\frac{20}{3}-\frac{4\times 6+5}{6}}{\frac{4\times 5+5}{5}\times 2-\frac{3\times 2+1}{2}}$$

Multiply 4 and 6 to get 24.

$$\frac{\frac{20}{3}-\frac{24+5}{6}}{\frac{4\times 5+5}{5}\times 2-\frac{3\times 2+1}{2}}$$

Add 24 and 5 to get 29.

$$\frac{\frac{20}{3}-\frac{29}{6}}{\frac{4\times 5+5}{5}\times 2-\frac{3\times 2+1}{2}}$$

Least common multiple of 3 and 6 is 6. Convert \frac{20}{3} and \frac{29}{6} to fractions with denominator 6.

$$\frac{\frac{40}{6}-\frac{29}{6}}{\frac{4\times 5+5}{5}\times 2-\frac{3\times 2+1}{2}}$$

Since \frac{40}{6} and \frac{29}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{40-29}{6}}{\frac{4\times 5+5}{5}\times 2-\frac{3\times 2+1}{2}}$$

Subtract 29 from 40 to get 11.

$$\frac{\frac{11}{6}}{\frac{4\times 5+5}{5}\times 2-\frac{3\times 2+1}{2}}$$

Multiply 4 and 5 to get 20.

$$\frac{\frac{11}{6}}{\frac{20+5}{5}\times 2-\frac{3\times 2+1}{2}}$$

Add 20 and 5 to get 25.

$$\frac{\frac{11}{6}}{\frac{25}{5}\times 2-\frac{3\times 2+1}{2}}$$

Divide 25 by 5 to get 5.

$$\frac{\frac{11}{6}}{5\times 2-\frac{3\times 2+1}{2}}$$

Multiply 5 and 2 to get 10.

$$\frac{\frac{11}{6}}{10-\frac{3\times 2+1}{2}}$$

Multiply 3 and 2 to get 6.

$$\frac{\frac{11}{6}}{10-\frac{6+1}{2}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{11}{6}}{10-\frac{7}{2}}$$

Convert 10 to fraction \frac{20}{2}.

$$\frac{\frac{11}{6}}{\frac{20}{2}-\frac{7}{2}}$$

Since \frac{20}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11}{6}}{\frac{20-7}{2}}$$

Subtract 7 from 20 to get 13.

$$\frac{\frac{11}{6}}{\frac{13}{2}}$$

Divide \frac{11}{6} by \frac{13}{2} by multiplying \frac{11}{6} by the reciprocal of \frac{13}{2}.

$$\frac{11}{6}\times \frac{2}{13}$$

Multiply \frac{11}{6} times \frac{2}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 2}{6\times 13}$$

Do the multiplications in the fraction \frac{11\times 2}{6\times 13}.

$$\frac{22}{78}$$

Reduce the fraction \frac{22}{78} to lowest terms by extracting and canceling out 2.

$$\frac{11}{39}$$

Factor

$$\frac{11}{3 \cdot 13} = 0.28205128205128205$$