Solve -6/7+-7/10+-4/21+3/20

$$\frac { - 6 } { 7 } + \frac { - 7 } { 10 } + \frac { - 4 } { 21 } + \frac { 3 } { 20 }$$

Evaluate

$$-\frac{671}{420}\approx -1.597619048$$

Solution Steps

Fraction \frac{-6}{7} can be rewritten as -\frac{6}{7} by extracting the negative sign.

$$-\frac{6}{7}+\frac{-7}{10}+\frac{-4}{21}+\frac{3}{20}$$

Fraction \frac{-7}{10} can be rewritten as -\frac{7}{10} by extracting the negative sign.

$$-\frac{6}{7}-\frac{7}{10}+\frac{-4}{21}+\frac{3}{20}$$

Least common multiple of 7 and 10 is 70. Convert -\frac{6}{7} and \frac{7}{10} to fractions with denominator 70.

$$-\frac{60}{70}-\frac{49}{70}+\frac{-4}{21}+\frac{3}{20}$$

Since -\frac{60}{70} and \frac{49}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-60-49}{70}+\frac{-4}{21}+\frac{3}{20}$$

Subtract 49 from -60 to get -109.

$$-\frac{109}{70}+\frac{-4}{21}+\frac{3}{20}$$

Fraction \frac{-4}{21} can be rewritten as -\frac{4}{21} by extracting the negative sign.

$$-\frac{109}{70}-\frac{4}{21}+\frac{3}{20}$$

Least common multiple of 70 and 21 is 210. Convert -\frac{109}{70} and \frac{4}{21} to fractions with denominator 210.

$$-\frac{327}{210}-\frac{40}{210}+\frac{3}{20}$$

Since -\frac{327}{210} and \frac{40}{210} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-327-40}{210}+\frac{3}{20}$$

Subtract 40 from -327 to get -367.

$$-\frac{367}{210}+\frac{3}{20}$$

Least common multiple of 210 and 20 is 420. Convert -\frac{367}{210} and \frac{3}{20} to fractions with denominator 420.

$$-\frac{734}{420}+\frac{63}{420}$$

Since -\frac{734}{420} and \frac{63}{420} have the same denominator, add them by adding their numerators.

$$\frac{-734+63}{420}$$

Add -734 and 63 to get -671.

$$-\frac{671}{420}$$

Factor

$$-\frac{671}{420} = -1\frac{251}{420} = -1.5976190476190477$$