Solve ((7*6*5*4*3)-6!)div(7!+6!)

$$((7 \times 6 \times 5 \times 4 \times 3)-6 ! ) \div (7 ! +6 ! )$$

Evaluate

$$\frac{5}{16}=0.3125$$

Solution Steps

Multiply 7 and 6 to get 42.

$$\frac{42\times 5\times 4\times 3-6!}{7!+6!}$$

Multiply 42 and 5 to get 210.

$$\frac{210\times 4\times 3-6!}{7!+6!}$$

Multiply 210 and 4 to get 840.

$$\frac{840\times 3-6!}{7!+6!}$$

Multiply 840 and 3 to get 2520.

$$\frac{2520-6!}{7!+6!}$$

The factorial of 6 is 720.

$$\frac{2520-720}{7!+6!}$$

Subtract 720 from 2520 to get 1800.

$$\frac{1800}{7!+6!}$$

The factorial of 7 is 5040.

$$\frac{1800}{5040+6!}$$

The factorial of 6 is 720.

$$\frac{1800}{5040+720}$$

Add 5040 and 720 to get 5760.

$$\frac{1800}{5760}$$

Reduce the fraction \frac{1800}{5760} to lowest terms by extracting and canceling out 360.

$$\frac{5}{16}$$

Factor

$$\frac{5}{2 ^ {4}} = 0.3125$$