Solve 24/27div111/21*35/9

$$2 \frac { 4 } { 27 } \div 1 \frac { 11 } { 21 } \times 3 \frac { 5 } { 9 }$$

Evaluate

$$\frac{406}{81}\approx 5.012345679$$

Solution Steps

Divide \frac{2\times 27+4}{27} by \frac{1\times 21+11}{21} by multiplying \frac{2\times 27+4}{27} by the reciprocal of \frac{1\times 21+11}{21}.

$$\frac{\left(2\times 27+4\right)\times 21}{27\left(1\times 21+11\right)}\times \frac{3\times 9+5}{9}$$

Cancel out 3 in both numerator and denominator.

$$\frac{7\left(4+2\times 27\right)}{9\left(11+21\right)}\times \frac{3\times 9+5}{9}$$

Multiply 2 and 27 to get 54.

$$\frac{7\left(4+54\right)}{9\left(11+21\right)}\times \frac{3\times 9+5}{9}$$

Add 4 and 54 to get 58.

$$\frac{7\times 58}{9\left(11+21\right)}\times \frac{3\times 9+5}{9}$$

Multiply 7 and 58 to get 406.

$$\frac{406}{9\left(11+21\right)}\times \frac{3\times 9+5}{9}$$

Add 11 and 21 to get 32.

$$\frac{406}{9\times 32}\times \frac{3\times 9+5}{9}$$

Multiply 9 and 32 to get 288.

$$\frac{406}{288}\times \frac{3\times 9+5}{9}$$

Reduce the fraction \frac{406}{288} to lowest terms by extracting and canceling out 2.

$$\frac{203}{144}\times \frac{3\times 9+5}{9}$$

Multiply 3 and 9 to get 27.

$$\frac{203}{144}\times \frac{27+5}{9}$$

Add 27 and 5 to get 32.

$$\frac{203}{144}\times \frac{32}{9}$$

Multiply \frac{203}{144} times \frac{32}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{203\times 32}{144\times 9}$$

Do the multiplications in the fraction \frac{203\times 32}{144\times 9}.

$$\frac{6496}{1296}$$

Reduce the fraction \frac{6496}{1296} to lowest terms by extracting and canceling out 16.

$$\frac{406}{81}$$

Factor

$$\frac{2 \cdot 7 \cdot 29}{3 ^ {4}} = 5\frac{1}{81} = 5.012345679012346$$