Solve (46.6/10+25.1^2/10+23.9^2/10+20^2/10-334.084)div3

$$( \frac{ 46.6 }{ 10 } + \frac{ { 25.1 }^{ 2 } }{ 10 } + \frac{ { 23.9 }^{ 2 } }{ 10 } + \frac{ { 20 }^{ 2 } }{ 10 } -334.084) \div 3$$

Evaluate

$$-56.434$$

Solution Steps

Expand \frac{46.6}{10} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{466}{100}+\frac{25.1^{2}}{10}+\frac{23.9^{2}}{10}+\frac{20^{2}}{10}-334.084}{3}$$

Reduce the fraction \frac{466}{100} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{233}{50}+\frac{25.1^{2}}{10}+\frac{23.9^{2}}{10}+\frac{20^{2}}{10}-334.084}{3}$$

Calculate 25.1 to the power of 2 and get 630.01.

$$\frac{\frac{233}{50}+\frac{630.01}{10}+\frac{23.9^{2}}{10}+\frac{20^{2}}{10}-334.084}{3}$$

Expand \frac{630.01}{10} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{233}{50}+\frac{63001}{1000}+\frac{23.9^{2}}{10}+\frac{20^{2}}{10}-334.084}{3}$$

Least common multiple of 50 and 1000 is 1000. Convert \frac{233}{50} and \frac{63001}{1000} to fractions with denominator 1000.

$$\frac{\frac{4660}{1000}+\frac{63001}{1000}+\frac{23.9^{2}}{10}+\frac{20^{2}}{10}-334.084}{3}$$

Since \frac{4660}{1000} and \frac{63001}{1000} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4660+63001}{1000}+\frac{23.9^{2}}{10}+\frac{20^{2}}{10}-334.084}{3}$$

Add 4660 and 63001 to get 67661.

$$\frac{\frac{67661}{1000}+\frac{23.9^{2}}{10}+\frac{20^{2}}{10}-334.084}{3}$$

Calculate 23.9 to the power of 2 and get 571.21.

$$\frac{\frac{67661}{1000}+\frac{571.21}{10}+\frac{20^{2}}{10}-334.084}{3}$$

Expand \frac{571.21}{10} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{67661}{1000}+\frac{57121}{1000}+\frac{20^{2}}{10}-334.084}{3}$$

Since \frac{67661}{1000} and \frac{57121}{1000} have the same denominator, add them by adding their numerators.

$$\frac{\frac{67661+57121}{1000}+\frac{20^{2}}{10}-334.084}{3}$$

Add 67661 and 57121 to get 124782.

$$\frac{\frac{124782}{1000}+\frac{20^{2}}{10}-334.084}{3}$$

Reduce the fraction \frac{124782}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{62391}{500}+\frac{20^{2}}{10}-334.084}{3}$$

Calculate 20 to the power of 2 and get 400.

$$\frac{\frac{62391}{500}+\frac{400}{10}-334.084}{3}$$

Divide 400 by 10 to get 40.

$$\frac{\frac{62391}{500}+40-334.084}{3}$$

Convert 40 to fraction \frac{20000}{500}.

$$\frac{\frac{62391}{500}+\frac{20000}{500}-334.084}{3}$$

Since \frac{62391}{500} and \frac{20000}{500} have the same denominator, add them by adding their numerators.

$$\frac{\frac{62391+20000}{500}-334.084}{3}$$

Add 62391 and 20000 to get 82391.

$$\frac{\frac{82391}{500}-334.084}{3}$$

Convert decimal number 334.084 to fraction \frac{334084}{1000}. Reduce the fraction \frac{334084}{1000} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{82391}{500}-\frac{83521}{250}}{3}$$

Least common multiple of 500 and 250 is 500. Convert \frac{82391}{500} and \frac{83521}{250} to fractions with denominator 500.

$$\frac{\frac{82391}{500}-\frac{167042}{500}}{3}$$

Since \frac{82391}{500} and \frac{167042}{500} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{82391-167042}{500}}{3}$$

Subtract 167042 from 82391 to get -84651.

$$\frac{-\frac{84651}{500}}{3}$$

Express \frac{-\frac{84651}{500}}{3} as a single fraction.

$$\frac{-84651}{500\times 3}$$

Multiply 500 and 3 to get 1500.

$$\frac{-84651}{1500}$$

Reduce the fraction \frac{-84651}{1500} to lowest terms by extracting and canceling out 3.

$$-\frac{28217}{500}$$

Factor

$$-56.434$$