Solve 31/9div111/21

$$3 \frac { 1 } { 9 } \div 1 \frac { 11 } { 21 }$$

Evaluate

$$\frac{49}{24}\approx 2.041666667$$

Solution Steps

Divide \frac{3\times 9+1}{9} by \frac{1\times 21+11}{21} by multiplying \frac{3\times 9+1}{9} by the reciprocal of \frac{1\times 21+11}{21}.

$$\frac{\left(3\times 9+1\right)\times 21}{9\left(1\times 21+11\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{7\left(1+3\times 9\right)}{3\left(11+21\right)}$$

Multiply 3 and 9 to get 27.

$$\frac{7\left(1+27\right)}{3\left(11+21\right)}$$

Add 1 and 27 to get 28.

$$\frac{7\times 28}{3\left(11+21\right)}$$

Multiply 7 and 28 to get 196.

$$\frac{196}{3\left(11+21\right)}$$

Add 11 and 21 to get 32.

$$\frac{196}{3\times 32}$$

Multiply 3 and 32 to get 96.

$$\frac{196}{96}$$

Reduce the fraction \frac{196}{96} to lowest terms by extracting and canceling out 4.

$$\frac{49}{24}$$

Factor

$$\frac{7 ^ {2}}{2 ^ {3} \cdot 3} = 2\frac{1}{24} = 2.0416666666666665$$