Solve -12/5+-7/20+3/14+1/7+frac{-1}{10}

$$\frac { - 12 } { 5 } + \frac { - 7 } { 20 } + \frac { 3 } { 14 } + \frac { 1 } { 7 } + \frac { - 1 } { 10 }$$

Evaluate

$$-\frac{349}{140}\approx -2.492857143$$

Solution Steps

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

$$-\frac{12}{5}+\frac{-7}{20}+\frac{3}{14}+\frac{1}{7}+\frac{-1}{10}$$

Fraction \frac{-7}{20} can be rewritten as -\frac{7}{20} by extracting the negative sign.

$$-\frac{12}{5}-\frac{7}{20}+\frac{3}{14}+\frac{1}{7}+\frac{-1}{10}$$

Least common multiple of 5 and 20 is 20. Convert -\frac{12}{5} and \frac{7}{20} to fractions with denominator 20.

$$-\frac{48}{20}-\frac{7}{20}+\frac{3}{14}+\frac{1}{7}+\frac{-1}{10}$$

Since -\frac{48}{20} and \frac{7}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-48-7}{20}+\frac{3}{14}+\frac{1}{7}+\frac{-1}{10}$$

Subtract 7 from -48 to get -55.

$$\frac{-55}{20}+\frac{3}{14}+\frac{1}{7}+\frac{-1}{10}$$

Reduce the fraction \frac{-55}{20} to lowest terms by extracting and canceling out 5.

$$-\frac{11}{4}+\frac{3}{14}+\frac{1}{7}+\frac{-1}{10}$$

Least common multiple of 4 and 14 is 28. Convert -\frac{11}{4} and \frac{3}{14} to fractions with denominator 28.

$$-\frac{77}{28}+\frac{6}{28}+\frac{1}{7}+\frac{-1}{10}$$

Since -\frac{77}{28} and \frac{6}{28} have the same denominator, add them by adding their numerators.

$$\frac{-77+6}{28}+\frac{1}{7}+\frac{-1}{10}$$

Add -77 and 6 to get -71.

$$-\frac{71}{28}+\frac{1}{7}+\frac{-1}{10}$$

Least common multiple of 28 and 7 is 28. Convert -\frac{71}{28} and \frac{1}{7} to fractions with denominator 28.

$$-\frac{71}{28}+\frac{4}{28}+\frac{-1}{10}$$

Since -\frac{71}{28} and \frac{4}{28} have the same denominator, add them by adding their numerators.

$$\frac{-71+4}{28}+\frac{-1}{10}$$

Add -71 and 4 to get -67.

$$-\frac{67}{28}+\frac{-1}{10}$$

Fraction \frac{-1}{10} can be rewritten as -\frac{1}{10} by extracting the negative sign.

$$-\frac{67}{28}-\frac{1}{10}$$

Least common multiple of 28 and 10 is 140. Convert -\frac{67}{28} and \frac{1}{10} to fractions with denominator 140.

$$-\frac{335}{140}-\frac{14}{140}$$

Since -\frac{335}{140} and \frac{14}{140} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-335-14}{140}$$

Subtract 14 from -335 to get -349.

$$-\frac{349}{140}$$

Factor

$$-\frac{349}{140} = -2\frac{69}{140} = -2.492857142857143$$