Solve 105/12div11/4*21/5

$$10 \frac { 5 } { 12 } \div 1 \frac { 1 } { 4 } \times 2 \frac { 1 } { 5 }$$

Evaluate

$$\frac{55}{3}\approx 18.333333333$$

Solution Steps

Divide \frac{10\times 12+5}{12} by \frac{1\times 4+1}{4} by multiplying \frac{10\times 12+5}{12} by the reciprocal of \frac{1\times 4+1}{4}.

$$\frac{\left(10\times 12+5\right)\times 4}{12\left(1\times 4+1\right)}\times \frac{2\times 5+1}{5}$$

Cancel out 4 in both numerator and denominator.

$$\frac{5+10\times 12}{3\left(1+4\right)}\times \frac{2\times 5+1}{5}$$

Multiply 10 and 12 to get 120.

$$\frac{5+120}{3\left(1+4\right)}\times \frac{2\times 5+1}{5}$$

Add 5 and 120 to get 125.

$$\frac{125}{3\left(1+4\right)}\times \frac{2\times 5+1}{5}$$

Add 1 and 4 to get 5.

$$\frac{125}{3\times 5}\times \frac{2\times 5+1}{5}$$

Multiply 3 and 5 to get 15.

$$\frac{125}{15}\times \frac{2\times 5+1}{5}$$

Reduce the fraction \frac{125}{15} to lowest terms by extracting and canceling out 5.

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

Multiply 2 and 5 to get 10.

$$\frac{25}{3}\times \frac{10+1}{5}$$

Add 10 and 1 to get 11.

$$\frac{25}{3}\times \frac{11}{5}$$

Multiply \frac{25}{3} times \frac{11}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 11}{3\times 5}$$

Do the multiplications in the fraction \frac{25\times 11}{3\times 5}.

$$\frac{275}{15}$$

Reduce the fraction \frac{275}{15} to lowest terms by extracting and canceling out 5.

$$\frac{55}{3}$$

Factor

$$\frac{5 \cdot 11}{3} = 18\frac{1}{3} = 18.333333333333332$$