Solve 8!-9*8*7*6*5/2*8*7*6*5*4+4*8*7*6*5

$$\frac{ 8 ! -9 \times 8 \times 7 \times 6 \times 5 }{ 2 \times 8 \times 7 \times 6 \times 5 \times 4+4 \times 8 \times 7 \times 6 \times 5 }$$

Evaluate

$$\frac{5}{4}=1.25$$

Solution Steps

The factorial of 8 is 40320.

$$\frac{40320-9\times 8\times 7\times 6\times 5}{2\times 8\times 7\times 6\times 5\times 4+4\times 8\times 7\times 6\times 5}$$

Multiply 9 and 8 to get 72.

$$\frac{40320-72\times 7\times 6\times 5}{2\times 8\times 7\times 6\times 5\times 4+4\times 8\times 7\times 6\times 5}$$

Multiply 72 and 7 to get 504.

$$\frac{40320-504\times 6\times 5}{2\times 8\times 7\times 6\times 5\times 4+4\times 8\times 7\times 6\times 5}$$

Multiply 504 and 6 to get 3024.

$$\frac{40320-3024\times 5}{2\times 8\times 7\times 6\times 5\times 4+4\times 8\times 7\times 6\times 5}$$

Multiply 3024 and 5 to get 15120.

$$\frac{40320-15120}{2\times 8\times 7\times 6\times 5\times 4+4\times 8\times 7\times 6\times 5}$$

Subtract 15120 from 40320 to get 25200.

$$\frac{25200}{2\times 8\times 7\times 6\times 5\times 4+4\times 8\times 7\times 6\times 5}$$

Multiply 2 and 8 to get 16. Multiply 4 and 8 to get 32.

$$\frac{25200}{16\times 7\times 6\times 5\times 4+32\times 7\times 6\times 5}$$

Multiply 16 and 7 to get 112.

$$\frac{25200}{112\times 6\times 5\times 4+32\times 7\times 6\times 5}$$

Multiply 112 and 6 to get 672.

$$\frac{25200}{672\times 5\times 4+32\times 7\times 6\times 5}$$

Multiply 672 and 5 to get 3360.

$$\frac{25200}{3360\times 4+32\times 7\times 6\times 5}$$

Multiply 3360 and 4 to get 13440.

$$\frac{25200}{13440+32\times 7\times 6\times 5}$$

Multiply 32 and 7 to get 224.

$$\frac{25200}{13440+224\times 6\times 5}$$

Multiply 224 and 6 to get 1344.

$$\frac{25200}{13440+1344\times 5}$$

Multiply 1344 and 5 to get 6720.

$$\frac{25200}{13440+6720}$$

Add 13440 and 6720 to get 20160.

$$\frac{25200}{20160}$$

Reduce the fraction \frac{25200}{20160} to lowest terms by extracting and canceling out 5040.

$$\frac{5}{4}$$

Factor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$