Solve -7/5+3-30/21+1/7-4/5-frac{2}{7}+frac{1}{5}

$$- \frac{ 7 }{ 5 } +3- \frac{ 30 }{ 21 } + \frac{ 1 }{ 7 } - \frac{ 4 }{ 5 } - \frac{ 2 }{ 7 } + \frac{ 1 }{ 5 }$$

Evaluate

$$-\frac{4}{7}\approx -0.571428571$$

Solution Steps

Convert 3 to fraction \frac{15}{5}.

$$-\frac{7}{5}+\frac{15}{5}-\frac{30}{21}+\frac{1}{7}-\frac{4}{5}-\frac{2}{7}+\frac{1}{5}$$

Since -\frac{7}{5} and \frac{15}{5} have the same denominator, add them by adding their numerators.

$$\frac{-7+15}{5}-\frac{30}{21}+\frac{1}{7}-\frac{4}{5}-\frac{2}{7}+\frac{1}{5}$$

Add -7 and 15 to get 8.

$$\frac{8}{5}-\frac{30}{21}+\frac{1}{7}-\frac{4}{5}-\frac{2}{7}+\frac{1}{5}$$

Reduce the fraction \frac{30}{21} to lowest terms by extracting and canceling out 3.

$$\frac{8}{5}-\frac{10}{7}+\frac{1}{7}-\frac{4}{5}-\frac{2}{7}+\frac{1}{5}$$

Least common multiple of 5 and 7 is 35. Convert \frac{8}{5} and \frac{10}{7} to fractions with denominator 35.

$$\frac{56}{35}-\frac{50}{35}+\frac{1}{7}-\frac{4}{5}-\frac{2}{7}+\frac{1}{5}$$

Since \frac{56}{35} and \frac{50}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{56-50}{35}+\frac{1}{7}-\frac{4}{5}-\frac{2}{7}+\frac{1}{5}$$

Subtract 50 from 56 to get 6.

$$\frac{6}{35}+\frac{1}{7}-\frac{4}{5}-\frac{2}{7}+\frac{1}{5}$$

Least common multiple of 35 and 7 is 35. Convert \frac{6}{35} and \frac{1}{7} to fractions with denominator 35.

$$\frac{6}{35}+\frac{5}{35}-\frac{4}{5}-\frac{2}{7}+\frac{1}{5}$$

Since \frac{6}{35} and \frac{5}{35} have the same denominator, add them by adding their numerators.

$$\frac{6+5}{35}-\frac{4}{5}-\frac{2}{7}+\frac{1}{5}$$

Add 6 and 5 to get 11.

$$\frac{11}{35}-\frac{4}{5}-\frac{2}{7}+\frac{1}{5}$$

Least common multiple of 35 and 5 is 35. Convert \frac{11}{35} and \frac{4}{5} to fractions with denominator 35.

$$\frac{11}{35}-\frac{28}{35}-\frac{2}{7}+\frac{1}{5}$$

Since \frac{11}{35} and \frac{28}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-28}{35}-\frac{2}{7}+\frac{1}{5}$$

Subtract 28 from 11 to get -17.

$$-\frac{17}{35}-\frac{2}{7}+\frac{1}{5}$$

Least common multiple of 35 and 7 is 35. Convert -\frac{17}{35} and \frac{2}{7} to fractions with denominator 35.

$$-\frac{17}{35}-\frac{10}{35}+\frac{1}{5}$$

Since -\frac{17}{35} and \frac{10}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-17-10}{35}+\frac{1}{5}$$

Subtract 10 from -17 to get -27.

$$-\frac{27}{35}+\frac{1}{5}$$

Least common multiple of 35 and 5 is 35. Convert -\frac{27}{35} and \frac{1}{5} to fractions with denominator 35.

$$-\frac{27}{35}+\frac{7}{35}$$

Since -\frac{27}{35} and \frac{7}{35} have the same denominator, add them by adding their numerators.

$$\frac{-27+7}{35}$$

Add -27 and 7 to get -20.

$$\frac{-20}{35}$$

Reduce the fraction \frac{-20}{35} to lowest terms by extracting and canceling out 5.

$$-\frac{4}{7}$$

Factor

$$-\frac{4}{7} = -0.5714285714285714$$