Solve 21/12div55/8*21/4

$$2 \frac { 1 } { 12 } \div 5 \frac { 5 } { 8 } \times 2 \frac { 1 } { 4 }$$

Evaluate

$$\frac{5}{6}\approx 0.833333333$$

Solution Steps

Divide \frac{2\times 12+1}{12} by \frac{5\times 8+5}{8} by multiplying \frac{2\times 12+1}{12} by the reciprocal of \frac{5\times 8+5}{8}.

$$\frac{\left(2\times 12+1\right)\times 8}{12\left(5\times 8+5\right)}\times \frac{2\times 4+1}{4}$$

Cancel out 4 in both numerator and denominator.

$$\frac{2\left(1+2\times 12\right)}{3\left(5+5\times 8\right)}\times \frac{2\times 4+1}{4}$$

Multiply 2 and 12 to get 24.

$$\frac{2\left(1+24\right)}{3\left(5+5\times 8\right)}\times \frac{2\times 4+1}{4}$$

Add 1 and 24 to get 25.

$$\frac{2\times 25}{3\left(5+5\times 8\right)}\times \frac{2\times 4+1}{4}$$

Multiply 2 and 25 to get 50.

$$\frac{50}{3\left(5+5\times 8\right)}\times \frac{2\times 4+1}{4}$$

Multiply 5 and 8 to get 40.

$$\frac{50}{3\left(5+40\right)}\times \frac{2\times 4+1}{4}$$

Add 5 and 40 to get 45.

$$\frac{50}{3\times 45}\times \frac{2\times 4+1}{4}$$

Multiply 3 and 45 to get 135.

$$\frac{50}{135}\times \frac{2\times 4+1}{4}$$

Reduce the fraction \frac{50}{135} to lowest terms by extracting and canceling out 5.

$$\frac{10}{27}\times \frac{2\times 4+1}{4}$$

Multiply 2 and 4 to get 8.

$$\frac{10}{27}\times \frac{8+1}{4}$$

Add 8 and 1 to get 9.

$$\frac{10}{27}\times \frac{9}{4}$$

Multiply \frac{10}{27} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 9}{27\times 4}$$

Do the multiplications in the fraction \frac{10\times 9}{27\times 4}.

$$\frac{90}{108}$$

Reduce the fraction \frac{90}{108} to lowest terms by extracting and canceling out 18.

$$\frac{5}{6}$$

Factor

$$\frac{5}{2 \cdot 3} = 0.8333333333333334$$