Solve 15*14*13*5*4/3*2*2/frac{20*19*18*17*16{5*4*3*2*1}}

$$\frac{ \frac{ 15 \times 14 \times 13 \times 5 \times 4 }{ 3 \times 2 \times 2 } }{ \frac{ 20 \times 19 \times 18 \times 17 \times 16 }{ 5 \times 4 \times 3 \times 2 \times 1 } }$$

Evaluate

$$\frac{2275}{7752}\approx 0.293472652$$

Solution Steps

Divide \frac{15\times 14\times 13\times 5\times 4}{3\times 2\times 2} by \frac{20\times 19\times 18\times 17\times 16}{5\times 4\times 3\times 2\times 1} by multiplying \frac{15\times 14\times 13\times 5\times 4}{3\times 2\times 2} by the reciprocal of \frac{20\times 19\times 18\times 17\times 16}{5\times 4\times 3\times 2\times 1}.

$$\frac{15\times 14\times 13\times 5\times 4\times 5\times 4\times 3\times 2\times 1}{3\times 2\times 2\times 20\times 19\times 18\times 17\times 16}$$

Cancel out 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 5 in both numerator and denominator.

$$\frac{5\times 5\times 7\times 13}{3\times 8\times 17\times 19}$$

Multiply 5 and 5 to get 25.

$$\frac{25\times 7\times 13}{3\times 8\times 17\times 19}$$

Multiply 25 and 7 to get 175.

$$\frac{175\times 13}{3\times 8\times 17\times 19}$$

Multiply 175 and 13 to get 2275.

$$\frac{2275}{3\times 8\times 17\times 19}$$

Multiply 3 and 8 to get 24.

$$\frac{2275}{24\times 17\times 19}$$

Multiply 24 and 17 to get 408.

$$\frac{2275}{408\times 19}$$

Multiply 408 and 19 to get 7752.

$$\frac{2275}{7752}$$

Factor

$$\frac{5 ^ {2} \cdot 7 \cdot 13}{2 ^ {3} \cdot 3 \cdot 17 \cdot 19} = 0.29347265221878227$$