Solve -2/3+(-2/7)*12/5-1/5

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

Evaluate

$$-\frac{19}{15}\approx -1.266666667$$

Solution Steps

Multiply 1 and 5 to get 5.

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

Add 5 and 2 to get 7.

$$-\frac{2}{3}-\frac{2}{7}\times \frac{7}{5}-\frac{1}{5}$$

Multiply -\frac{2}{7} times \frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 7 in both numerator and denominator.

$$-\frac{2}{3}+\frac{-2}{5}-\frac{1}{5}$$

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

$$-\frac{2}{3}-\frac{2}{5}-\frac{1}{5}$$

Least common multiple of 3 and 5 is 15. Convert -\frac{2}{3} and \frac{2}{5} to fractions with denominator 15.

$$-\frac{10}{15}-\frac{6}{15}-\frac{1}{5}$$

Since -\frac{10}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-10-6}{15}-\frac{1}{5}$$

Subtract 6 from -10 to get -16.

$$-\frac{16}{15}-\frac{1}{5}$$

Least common multiple of 15 and 5 is 15. Convert -\frac{16}{15} and \frac{1}{5} to fractions with denominator 15.

$$-\frac{16}{15}-\frac{3}{15}$$

Since -\frac{16}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-16-3}{15}$$

Subtract 3 from -16 to get -19.

$$-\frac{19}{15}$$

Factor

$$-\frac{19}{15} = -1\frac{4}{15} = -1.2666666666666666$$