Solve 21/3div11/6*31/4div11/3

$$2 \frac { 1 } { 3 } \div 1 \frac { 1 } { 6 } \times 3 \frac { 1 } { 4 } \div 1 \frac { 1 } { 3 }$$

Evaluate

$$\frac{39}{8}=4.875$$

Solution Steps

Divide \frac{2\times 3+1}{3} by \frac{1\times 6+1}{6} by multiplying \frac{2\times 3+1}{3} by the reciprocal of \frac{1\times 6+1}{6}.

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

Cancel out 3 in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

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

Add 1 and 6 to get 7.

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

Multiply 2 and 7 to get 14.

$$\frac{\frac{14}{1+6}\times \frac{3\times 4+1}{4}}{\frac{1\times 3+1}{3}}$$

Add 1 and 6 to get 7.

$$\frac{\frac{14}{7}\times \frac{3\times 4+1}{4}}{\frac{1\times 3+1}{3}}$$

Divide 14 by 7 to get 2.

$$\frac{2\times \frac{3\times 4+1}{4}}{\frac{1\times 3+1}{3}}$$

Multiply 3 and 4 to get 12.

$$\frac{2\times \frac{12+1}{4}}{\frac{1\times 3+1}{3}}$$

Add 12 and 1 to get 13.

$$\frac{2\times \frac{13}{4}}{\frac{1\times 3+1}{3}}$$

Express 2\times \frac{13}{4} as a single fraction.

$$\frac{\frac{2\times 13}{4}}{\frac{1\times 3+1}{3}}$$

Multiply 2 and 13 to get 26.

$$\frac{\frac{26}{4}}{\frac{1\times 3+1}{3}}$$

Reduce the fraction \frac{26}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{13}{2}}{\frac{1\times 3+1}{3}}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{13}{2}}{\frac{3+1}{3}}$$

Add 3 and 1 to get 4.

$$\frac{\frac{13}{2}}{\frac{4}{3}}$$

Divide \frac{13}{2} by \frac{4}{3} by multiplying \frac{13}{2} by the reciprocal of \frac{4}{3}.

$$\frac{13}{2}\times \frac{3}{4}$$

Multiply \frac{13}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 3}{2\times 4}$$

Do the multiplications in the fraction \frac{13\times 3}{2\times 4}.

$$\frac{39}{8}$$

Factor

$$\frac{3 \cdot 13}{2 ^ {3}} = 4\frac{7}{8} = 4.875$$