Solve 5(26!)+(27!)/4(27!)-8(26!)

$$\frac { 5 ( 26 ! ) + ( 27 ! ) } { 4 ( 27 ! ) - 8 ( 26 ! ) }$$

Evaluate

$$\frac{8}{25}=0.32$$

Solution Steps

The factorial of 26 is 403291461126605635584000000.

$$\frac{5\times 403291461126605635584000000+27!}{4\times 27!-8\times 26!}$$

Multiply 5 and 403291461126605635584000000 to get 2016457305633028177920000000.

$$\frac{2016457305633028177920000000+27!}{4\times 27!-8\times 26!}$$

The factorial of 27 is 10888869450418352160768000000.

$$\frac{2016457305633028177920000000+10888869450418352160768000000}{4\times 27!-8\times 26!}$$

Add 2016457305633028177920000000 and 10888869450418352160768000000 to get 12905326756051380338688000000.

$$\frac{12905326756051380338688000000}{4\times 27!-8\times 26!}$$

The factorial of 27 is 10888869450418352160768000000.

$$\frac{12905326756051380338688000000}{4\times 10888869450418352160768000000-8\times 26!}$$

Multiply 4 and 10888869450418352160768000000 to get 43555477801673408643072000000.

$$\frac{12905326756051380338688000000}{43555477801673408643072000000-8\times 26!}$$

The factorial of 26 is 403291461126605635584000000.

$$\frac{12905326756051380338688000000}{43555477801673408643072000000-8\times 403291461126605635584000000}$$

Multiply 8 and 403291461126605635584000000 to get 3226331689012845084672000000.

$$\frac{12905326756051380338688000000}{43555477801673408643072000000-3226331689012845084672000000}$$

Subtract 3226331689012845084672000000 from 43555477801673408643072000000 to get 40329146112660563558400000000.

$$\frac{12905326756051380338688000000}{40329146112660563558400000000}$$

Reduce the fraction \frac{12905326756051380338688000000}{40329146112660563558400000000} to lowest terms by extracting and canceling out 1613165844506422542336000000.

$$\frac{8}{25}$$

Factor

$$\frac{2 ^ {3}}{5 ^ {2}} = 0.32$$