Solve 16*3/12+1/frac{16+3*4{12+1+34}}

$$\frac { \frac { 16 \times 3 } { 12 + 1 } } { \frac { 16 + 3 \times 4 } { 12 + 1 + 34 } }$$

Evaluate

$$\frac{564}{91}\approx 6.197802198$$

Solution Steps

Divide \frac{16\times 3}{12+1} by \frac{16+3\times 4}{12+1+34} by multiplying \frac{16\times 3}{12+1} by the reciprocal of \frac{16+3\times 4}{12+1+34}.

$$\frac{16\times 3\left(12+1+34\right)}{\left(12+1\right)\left(16+3\times 4\right)}$$

Multiply 16 and 3 to get 48.

$$\frac{48\left(12+1+34\right)}{\left(12+1\right)\left(16+3\times 4\right)}$$

Add 12 and 1 to get 13.

$$\frac{48\left(13+34\right)}{\left(12+1\right)\left(16+3\times 4\right)}$$

Add 13 and 34 to get 47.

$$\frac{48\times 47}{\left(12+1\right)\left(16+3\times 4\right)}$$

Multiply 48 and 47 to get 2256.

$$\frac{2256}{\left(12+1\right)\left(16+3\times 4\right)}$$

Add 12 and 1 to get 13.

$$\frac{2256}{13\left(16+3\times 4\right)}$$

Multiply 3 and 4 to get 12.

$$\frac{2256}{13\left(16+12\right)}$$

Add 16 and 12 to get 28.

$$\frac{2256}{13\times 28}$$

Multiply 13 and 28 to get 364.

$$\frac{2256}{364}$$

Reduce the fraction \frac{2256}{364} to lowest terms by extracting and canceling out 4.

$$\frac{564}{91}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 47}{7 \cdot 13} = 6\frac{18}{91} = 6.197802197802198$$