Solve 31/3*2-42/6/4frac{5{6}*2-31/3}

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

Evaluate

$$\frac{7}{19}\approx 0.368421053$$

Solution Steps

Multiply 3 and 3 to get 9.

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

Add 9 and 1 to get 10.

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

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

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

Multiply 10 and 2 to get 20.

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

Multiply 4 and 6 to get 24.

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

Add 24 and 2 to get 26.

$$\frac{\frac{20}{3}-\frac{26}{6}}{\frac{4\times 6+5}{6}\times 2-\frac{3\times 3+1}{3}}$$

Reduce the fraction \frac{26}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{20}{3}-\frac{13}{3}}{\frac{4\times 6+5}{6}\times 2-\frac{3\times 3+1}{3}}$$

Since \frac{20}{3} and \frac{13}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{20-13}{3}}{\frac{4\times 6+5}{6}\times 2-\frac{3\times 3+1}{3}}$$

Subtract 13 from 20 to get 7.

$$\frac{\frac{7}{3}}{\frac{4\times 6+5}{6}\times 2-\frac{3\times 3+1}{3}}$$

Multiply 4 and 6 to get 24.

$$\frac{\frac{7}{3}}{\frac{24+5}{6}\times 2-\frac{3\times 3+1}{3}}$$

Add 24 and 5 to get 29.

$$\frac{\frac{7}{3}}{\frac{29}{6}\times 2-\frac{3\times 3+1}{3}}$$

Express \frac{29}{6}\times 2 as a single fraction.

$$\frac{\frac{7}{3}}{\frac{29\times 2}{6}-\frac{3\times 3+1}{3}}$$

Multiply 29 and 2 to get 58.

$$\frac{\frac{7}{3}}{\frac{58}{6}-\frac{3\times 3+1}{3}}$$

Reduce the fraction \frac{58}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{7}{3}}{\frac{29}{3}-\frac{3\times 3+1}{3}}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{7}{3}}{\frac{29}{3}-\frac{9+1}{3}}$$

Add 9 and 1 to get 10.

$$\frac{\frac{7}{3}}{\frac{29}{3}-\frac{10}{3}}$$

Since \frac{29}{3} and \frac{10}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{3}}{\frac{29-10}{3}}$$

Subtract 10 from 29 to get 19.

$$\frac{\frac{7}{3}}{\frac{19}{3}}$$

Divide \frac{7}{3} by \frac{19}{3} by multiplying \frac{7}{3} by the reciprocal of \frac{19}{3}.

$$\frac{7}{3}\times \frac{3}{19}$$

Multiply \frac{7}{3} times \frac{3}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 3}{3\times 19}$$

Cancel out 3 in both numerator and denominator.

$$\frac{7}{19}$$

Factor

$$\frac{7}{19} = 0.3684210526315789$$