Solve 10.2div4+6.3+3.4-8.2div4-6.8*5.5+9.3-1.4+16.4-20.8div4+5.8

$$10.2 \div 4+6.3+3.4-8.2 \div 4-6.8 \times 5.5+9.3-1.4+16.4-20.8 \div 4+5.8$$

Evaluate

$$-2.3$$

Solution Steps

Expand \frac{10.2}{4} by multiplying both numerator and the denominator by 10.

$$\frac{102}{40}+6.3+3.4-\frac{8.2}{4}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Reduce the fraction \frac{102}{40} to lowest terms by extracting and canceling out 2.

$$\frac{51}{20}+6.3+3.4-\frac{8.2}{4}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Convert decimal number 6.3 to fraction \frac{63}{10}.

$$\frac{51}{20}+\frac{63}{10}+3.4-\frac{8.2}{4}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Least common multiple of 20 and 10 is 20. Convert \frac{51}{20} and \frac{63}{10} to fractions with denominator 20.

$$\frac{51}{20}+\frac{126}{20}+3.4-\frac{8.2}{4}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Since \frac{51}{20} and \frac{126}{20} have the same denominator, add them by adding their numerators.

$$\frac{51+126}{20}+3.4-\frac{8.2}{4}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Add 51 and 126 to get 177.

$$\frac{177}{20}+3.4-\frac{8.2}{4}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Convert decimal number 3.4 to fraction \frac{34}{10}. Reduce the fraction \frac{34}{10} to lowest terms by extracting and canceling out 2.

$$\frac{177}{20}+\frac{17}{5}-\frac{8.2}{4}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Least common multiple of 20 and 5 is 20. Convert \frac{177}{20} and \frac{17}{5} to fractions with denominator 20.

$$\frac{177}{20}+\frac{68}{20}-\frac{8.2}{4}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Since \frac{177}{20} and \frac{68}{20} have the same denominator, add them by adding their numerators.

$$\frac{177+68}{20}-\frac{8.2}{4}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Add 177 and 68 to get 245.

$$\frac{245}{20}-\frac{8.2}{4}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Reduce the fraction \frac{245}{20} to lowest terms by extracting and canceling out 5.

$$\frac{49}{4}-\frac{8.2}{4}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Expand \frac{8.2}{4} by multiplying both numerator and the denominator by 10.

$$\frac{49}{4}-\frac{82}{40}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Reduce the fraction \frac{82}{40} to lowest terms by extracting and canceling out 2.

$$\frac{49}{4}-\frac{41}{20}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Least common multiple of 4 and 20 is 20. Convert \frac{49}{4} and \frac{41}{20} to fractions with denominator 20.

$$\frac{245}{20}-\frac{41}{20}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Since \frac{245}{20} and \frac{41}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{245-41}{20}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Subtract 41 from 245 to get 204.

$$\frac{204}{20}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Reduce the fraction \frac{204}{20} to lowest terms by extracting and canceling out 4.

$$\frac{51}{5}-6.8\times 5.5+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Multiply 6.8 and 5.5 to get 37.4.

$$\frac{51}{5}-37.4+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Convert decimal number 37.4 to fraction \frac{374}{10}. Reduce the fraction \frac{374}{10} to lowest terms by extracting and canceling out 2.

$$\frac{51}{5}-\frac{187}{5}+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Since \frac{51}{5} and \frac{187}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{51-187}{5}+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Subtract 187 from 51 to get -136.

$$-\frac{136}{5}+9.3-1.4+16.4-\frac{20.8}{4}+5.8$$

Convert decimal number 9.3 to fraction \frac{93}{10}.

$$-\frac{136}{5}+\frac{93}{10}-1.4+16.4-\frac{20.8}{4}+5.8$$

Least common multiple of 5 and 10 is 10. Convert -\frac{136}{5} and \frac{93}{10} to fractions with denominator 10.

$$-\frac{272}{10}+\frac{93}{10}-1.4+16.4-\frac{20.8}{4}+5.8$$

Since -\frac{272}{10} and \frac{93}{10} have the same denominator, add them by adding their numerators.

$$\frac{-272+93}{10}-1.4+16.4-\frac{20.8}{4}+5.8$$

Add -272 and 93 to get -179.

$$-\frac{179}{10}-1.4+16.4-\frac{20.8}{4}+5.8$$

Convert decimal number 1.4 to fraction \frac{14}{10}. Reduce the fraction \frac{14}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{179}{10}-\frac{7}{5}+16.4-\frac{20.8}{4}+5.8$$

Least common multiple of 10 and 5 is 10. Convert -\frac{179}{10} and \frac{7}{5} to fractions with denominator 10.

$$-\frac{179}{10}-\frac{14}{10}+16.4-\frac{20.8}{4}+5.8$$

Since -\frac{179}{10} and \frac{14}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-179-14}{10}+16.4-\frac{20.8}{4}+5.8$$

Subtract 14 from -179 to get -193.

$$-\frac{193}{10}+16.4-\frac{20.8}{4}+5.8$$

Convert decimal number 16.4 to fraction \frac{164}{10}. Reduce the fraction \frac{164}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{193}{10}+\frac{82}{5}-\frac{20.8}{4}+5.8$$

Least common multiple of 10 and 5 is 10. Convert -\frac{193}{10} and \frac{82}{5} to fractions with denominator 10.

$$-\frac{193}{10}+\frac{164}{10}-\frac{20.8}{4}+5.8$$

Since -\frac{193}{10} and \frac{164}{10} have the same denominator, add them by adding their numerators.

$$\frac{-193+164}{10}-\frac{20.8}{4}+5.8$$

Add -193 and 164 to get -29.

$$-\frac{29}{10}-\frac{20.8}{4}+5.8$$

Expand \frac{20.8}{4} by multiplying both numerator and the denominator by 10.

$$-\frac{29}{10}-\frac{208}{40}+5.8$$

Reduce the fraction \frac{208}{40} to lowest terms by extracting and canceling out 8.

$$-\frac{29}{10}-\frac{26}{5}+5.8$$

Least common multiple of 10 and 5 is 10. Convert -\frac{29}{10} and \frac{26}{5} to fractions with denominator 10.

$$-\frac{29}{10}-\frac{52}{10}+5.8$$

Since -\frac{29}{10} and \frac{52}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-29-52}{10}+5.8$$

Subtract 52 from -29 to get -81.

$$-\frac{81}{10}+5.8$$

Convert decimal number 5.8 to fraction \frac{58}{10}. Reduce the fraction \frac{58}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{81}{10}+\frac{29}{5}$$

Least common multiple of 10 and 5 is 10. Convert -\frac{81}{10} and \frac{29}{5} to fractions with denominator 10.

$$-\frac{81}{10}+\frac{58}{10}$$

Since -\frac{81}{10} and \frac{58}{10} have the same denominator, add them by adding their numerators.

$$\frac{-81+58}{10}$$

Add -81 and 58 to get -23.

$$-\frac{23}{10}$$

Factor

$$-2.3$$