Solve 25*1000div3600*5.663-0.5*0.2*9.81*5.663^2

$$25 \times 1000 \div 3600 \times 5.663-0.5 \times 0.2 \times 9.81 \times { 5.663 }^{ 2 }$$

Evaluate

$$\frac{70795275299}{9000000000}\approx 7.8661417$$

Solution Steps

Multiply 25 and 1000 to get 25000.

$$\frac{25000}{3600}\times 5.663-0.5\times 0.2\times 9.81\times 5.663^{2}$$

Reduce the fraction \frac{25000}{3600} to lowest terms by extracting and canceling out 200.

$$\frac{125}{18}\times 5.663-0.5\times 0.2\times 9.81\times 5.663^{2}$$

Convert decimal number 5.663 to fraction \frac{5663}{1000}.

$$\frac{125}{18}\times \frac{5663}{1000}-0.5\times 0.2\times 9.81\times 5.663^{2}$$

Multiply \frac{125}{18} times \frac{5663}{1000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{125\times 5663}{18\times 1000}-0.5\times 0.2\times 9.81\times 5.663^{2}$$

Do the multiplications in the fraction \frac{125\times 5663}{18\times 1000}.

$$\frac{707875}{18000}-0.5\times 0.2\times 9.81\times 5.663^{2}$$

Reduce the fraction \frac{707875}{18000} to lowest terms by extracting and canceling out 125.

$$\frac{5663}{144}-0.5\times 0.2\times 9.81\times 5.663^{2}$$

Multiply 0.5 and 0.2 to get 0.1.

$$\frac{5663}{144}-0.1\times 9.81\times 5.663^{2}$$

Multiply 0.1 and 9.81 to get 0.981.

$$\frac{5663}{144}-0.981\times 5.663^{2}$$

Calculate 5.663 to the power of 2 and get 32.069569.

$$\frac{5663}{144}-0.981\times 32.069569$$

Multiply 0.981 and 32.069569 to get 31.460247189.

$$\frac{5663}{144}-31.460247189$$

Convert decimal number 31.460247189 to fraction \frac{31460247189}{1000000000}.

$$\frac{5663}{144}-\frac{31460247189}{1000000000}$$

Least common multiple of 144 and 1000000000 is 9000000000. Convert \frac{5663}{144} and \frac{31460247189}{1000000000} to fractions with denominator 9000000000.

$$\frac{353937500000}{9000000000}-\frac{283142224701}{9000000000}$$

Since \frac{353937500000}{9000000000} and \frac{283142224701}{9000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{353937500000-283142224701}{9000000000}$$

Subtract 283142224701 from 353937500000 to get 70795275299.

$$\frac{70795275299}{9000000000}$$

Factor

$$\frac{7 \cdot 19 \cdot 239 \cdot 809 \cdot 2753}{2 ^ {9} \cdot 3 ^ {2} \cdot 5 ^ {9}} = 7\frac{7795275299}{9000000000} = 7.866141699888889$$