Solve -2/7+(-23/5)+12/7-(-3/5)

$$- \frac { 2 } { 7 } + ( - 2 \frac { 3 } { 5 } ) + 1 \frac { 2 } { 7 } - ( - \frac { 3 } { 5 } )$$

Evaluate

$$-1$$

Solution Steps

Multiply 2 and 5 to get 10.

$$-\frac{2}{7}-\frac{10+3}{5}+\frac{1\times 7+2}{7}-\left(-\frac{3}{5}\right)$$

Add 10 and 3 to get 13.

$$-\frac{2}{7}-\frac{13}{5}+\frac{1\times 7+2}{7}-\left(-\frac{3}{5}\right)$$

Least common multiple of 7 and 5 is 35. Convert -\frac{2}{7} and \frac{13}{5} to fractions with denominator 35.

$$-\frac{10}{35}-\frac{91}{35}+\frac{1\times 7+2}{7}-\left(-\frac{3}{5}\right)$$

Since -\frac{10}{35} and \frac{91}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-10-91}{35}+\frac{1\times 7+2}{7}-\left(-\frac{3}{5}\right)$$

Subtract 91 from -10 to get -101.

$$-\frac{101}{35}+\frac{1\times 7+2}{7}-\left(-\frac{3}{5}\right)$$

Multiply 1 and 7 to get 7.

$$-\frac{101}{35}+\frac{7+2}{7}-\left(-\frac{3}{5}\right)$$

Add 7 and 2 to get 9.

$$-\frac{101}{35}+\frac{9}{7}-\left(-\frac{3}{5}\right)$$

Least common multiple of 35 and 7 is 35. Convert -\frac{101}{35} and \frac{9}{7} to fractions with denominator 35.

$$-\frac{101}{35}+\frac{45}{35}-\left(-\frac{3}{5}\right)$$

Since -\frac{101}{35} and \frac{45}{35} have the same denominator, add them by adding their numerators.

$$\frac{-101+45}{35}-\left(-\frac{3}{5}\right)$$

Add -101 and 45 to get -56.

$$\frac{-56}{35}-\left(-\frac{3}{5}\right)$$

Reduce the fraction \frac{-56}{35} to lowest terms by extracting and canceling out 7.

$$-\frac{8}{5}-\left(-\frac{3}{5}\right)$$

The opposite of -\frac{3}{5} is \frac{3}{5}.

$$-\frac{8}{5}+\frac{3}{5}$$

Since -\frac{8}{5} and \frac{3}{5} have the same denominator, add them by adding their numerators.

$$\frac{-8+3}{5}$$

Add -8 and 3 to get -5.

$$\frac{-5}{5}$$

Divide -5 by 5 to get -1.

$$-1$$

Factor

$$-1$$