Solve 105.8*10.8-1/2*9.81*10.8^2

$$105.8 \times 10.8- \frac{ 1 }{ 2 } \times 9.81 \times { 10.8 }^{ 2 }$$

Evaluate

$$570.5208$$

Solution Steps

Multiply 105.8 and 10.8 to get 1142.64.

$$1142.64-\frac{1}{2}\times 9.81\times 10.8^{2}$$

Convert decimal number 9.81 to fraction \frac{981}{100}.

$$1142.64-\frac{1}{2}\times \frac{981}{100}\times 10.8^{2}$$

Multiply \frac{1}{2} times \frac{981}{100} by multiplying numerator times numerator and denominator times denominator.

$$1142.64-\frac{1\times 981}{2\times 100}\times 10.8^{2}$$

Do the multiplications in the fraction \frac{1\times 981}{2\times 100}.

$$1142.64-\frac{981}{200}\times 10.8^{2}$$

Calculate 10.8 to the power of 2 and get 116.64.

$$1142.64-\frac{981}{200}\times 116.64$$

Convert decimal number 116.64 to fraction \frac{11664}{100}. Reduce the fraction \frac{11664}{100} to lowest terms by extracting and canceling out 4.

$$1142.64-\frac{981}{200}\times \frac{2916}{25}$$

Multiply \frac{981}{200} times \frac{2916}{25} by multiplying numerator times numerator and denominator times denominator.

$$1142.64-\frac{981\times 2916}{200\times 25}$$

Do the multiplications in the fraction \frac{981\times 2916}{200\times 25}.

$$1142.64-\frac{2860596}{5000}$$

Reduce the fraction \frac{2860596}{5000} to lowest terms by extracting and canceling out 4.

$$1142.64-\frac{715149}{1250}$$

Convert decimal number 1142.64 to fraction \frac{114264}{100}. Reduce the fraction \frac{114264}{100} to lowest terms by extracting and canceling out 4.

$$\frac{28566}{25}-\frac{715149}{1250}$$

Least common multiple of 25 and 1250 is 1250. Convert \frac{28566}{25} and \frac{715149}{1250} to fractions with denominator 1250.

$$\frac{1428300}{1250}-\frac{715149}{1250}$$

Since \frac{1428300}{1250} and \frac{715149}{1250} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1428300-715149}{1250}$$

Subtract 715149 from 1428300 to get 713151.

$$\frac{713151}{1250}$$

Factor

$$\frac{61 \cdot 433 \cdot 3 ^ {3}}{2 \cdot 5 ^ {4}} = 570\frac{651}{1250} = 570.5208$$