Solve 9/10+-7/12+4/19+-5/12+frac{1}{10}

$$\frac { 9 } { 10 } + \frac { - 7 } { 12 } + \frac { 4 } { 19 } + \frac { - 5 } { 12 } + \frac { 1 } { 10 }$$

Evaluate

$$\frac{4}{19}\approx 0.210526316$$

Solution Steps

Fraction \frac{-7}{12} can be rewritten as -\frac{7}{12} by extracting the negative sign.

$$\frac{9}{10}-\frac{7}{12}+\frac{4}{19}+\frac{-5}{12}+\frac{1}{10}$$

Least common multiple of 10 and 12 is 60. Convert \frac{9}{10} and \frac{7}{12} to fractions with denominator 60.

$$\frac{54}{60}-\frac{35}{60}+\frac{4}{19}+\frac{-5}{12}+\frac{1}{10}$$

Since \frac{54}{60} and \frac{35}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{54-35}{60}+\frac{4}{19}+\frac{-5}{12}+\frac{1}{10}$$

Subtract 35 from 54 to get 19.

$$\frac{19}{60}+\frac{4}{19}+\frac{-5}{12}+\frac{1}{10}$$

Least common multiple of 60 and 19 is 1140. Convert \frac{19}{60} and \frac{4}{19} to fractions with denominator 1140.

$$\frac{361}{1140}+\frac{240}{1140}+\frac{-5}{12}+\frac{1}{10}$$

Since \frac{361}{1140} and \frac{240}{1140} have the same denominator, add them by adding their numerators.

$$\frac{361+240}{1140}+\frac{-5}{12}+\frac{1}{10}$$

Add 361 and 240 to get 601.

$$\frac{601}{1140}+\frac{-5}{12}+\frac{1}{10}$$

Fraction \frac{-5}{12} can be rewritten as -\frac{5}{12} by extracting the negative sign.

$$\frac{601}{1140}-\frac{5}{12}+\frac{1}{10}$$

Least common multiple of 1140 and 12 is 1140. Convert \frac{601}{1140} and \frac{5}{12} to fractions with denominator 1140.

$$\frac{601}{1140}-\frac{475}{1140}+\frac{1}{10}$$

Since \frac{601}{1140} and \frac{475}{1140} have the same denominator, subtract them by subtracting their numerators.

$$\frac{601-475}{1140}+\frac{1}{10}$$

Subtract 475 from 601 to get 126.

$$\frac{126}{1140}+\frac{1}{10}$$

Reduce the fraction \frac{126}{1140} to lowest terms by extracting and canceling out 6.

$$\frac{21}{190}+\frac{1}{10}$$

Least common multiple of 190 and 10 is 190. Convert \frac{21}{190} and \frac{1}{10} to fractions with denominator 190.

$$\frac{21}{190}+\frac{19}{190}$$

Since \frac{21}{190} and \frac{19}{190} have the same denominator, add them by adding their numerators.

$$\frac{21+19}{190}$$

Add 21 and 19 to get 40.

$$\frac{40}{190}$$

Reduce the fraction \frac{40}{190} to lowest terms by extracting and canceling out 10.

$$\frac{4}{19}$$

Factor

$$\frac{2 ^ {2}}{19} = 0.21052631578947367$$