Solve (5/7)+(4/5)-(2/7)+(1/5)]

$$( \frac { 5 } { 7 } ) + ( \frac { 4 } { 5 } ) - ( \frac { 2 } { 7 } ) + ( \frac { 1 } { 5 } ) ]$$

Evaluate

$$\frac{10}{7}\approx 1.428571429$$

Solution Steps

Least common multiple of 7 and 5 is 35. Convert \frac{5}{7} and \frac{4}{5} to fractions with denominator 35.

$$\frac{25}{35}+\frac{28}{35}-\frac{2}{7}+\frac{1}{5}$$

Since \frac{25}{35} and \frac{28}{35} have the same denominator, add them by adding their numerators.

$$\frac{25+28}{35}-\frac{2}{7}+\frac{1}{5}$$

Add 25 and 28 to get 53.

$$\frac{53}{35}-\frac{2}{7}+\frac{1}{5}$$

Least common multiple of 35 and 7 is 35. Convert \frac{53}{35} and \frac{2}{7} to fractions with denominator 35.

$$\frac{53}{35}-\frac{10}{35}+\frac{1}{5}$$

Since \frac{53}{35} and \frac{10}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{53-10}{35}+\frac{1}{5}$$

Subtract 10 from 53 to get 43.

$$\frac{43}{35}+\frac{1}{5}$$

Least common multiple of 35 and 5 is 35. Convert \frac{43}{35} and \frac{1}{5} to fractions with denominator 35.

$$\frac{43}{35}+\frac{7}{35}$$

Since \frac{43}{35} and \frac{7}{35} have the same denominator, add them by adding their numerators.

$$\frac{43+7}{35}$$

Add 43 and 7 to get 50.

$$\frac{50}{35}$$

Reduce the fraction \frac{50}{35} to lowest terms by extracting and canceling out 5.

$$\frac{10}{7}$$

Factor

$$\frac{2 \cdot 5}{7} = 1\frac{3}{7} = 1.4285714285714286$$