Solve (-3/7*1/5)+(-6/5*-5/9)

$$( \frac { - 3 } { 7 } \cdot \frac { 1 } { 5 } ) + ( \frac { - 6 } { 5 } \cdot \frac { - 5 } { 9 } )$$

Evaluate

$$\frac{61}{105}\approx 0.580952381$$

Solution Steps

Fraction \frac{-3}{7} can be rewritten as -\frac{3}{7} by extracting the negative sign.

$$-\frac{3}{7}\times \frac{1}{5}+\frac{-6}{5}\times \frac{-5}{9}$$

Multiply -\frac{3}{7} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3}{7\times 5}+\frac{-6}{5}\times \frac{-5}{9}$$

Do the multiplications in the fraction \frac{-3}{7\times 5}.

$$\frac{-3}{35}+\frac{-6}{5}\times \frac{-5}{9}$$

Fraction \frac{-3}{35} can be rewritten as -\frac{3}{35} by extracting the negative sign.

$$-\frac{3}{35}+\frac{-6}{5}\times \frac{-5}{9}$$

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

$$-\frac{3}{35}-\frac{6}{5}\times \frac{-5}{9}$$

Fraction \frac{-5}{9} can be rewritten as -\frac{5}{9} by extracting the negative sign.

$$-\frac{3}{35}-\frac{6}{5}\left(-\frac{5}{9}\right)$$

Multiply -\frac{6}{5} times -\frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{3}{35}+\frac{-6\left(-5\right)}{5\times 9}$$

Do the multiplications in the fraction \frac{-6\left(-5\right)}{5\times 9}.

$$-\frac{3}{35}+\frac{30}{45}$$

Reduce the fraction \frac{30}{45} to lowest terms by extracting and canceling out 15.

$$-\frac{3}{35}+\frac{2}{3}$$

Least common multiple of 35 and 3 is 105. Convert -\frac{3}{35} and \frac{2}{3} to fractions with denominator 105.

$$-\frac{9}{105}+\frac{70}{105}$$

Since -\frac{9}{105} and \frac{70}{105} have the same denominator, add them by adding their numerators.

$$\frac{-9+70}{105}$$

Add -9 and 70 to get 61.

$$\frac{61}{105}$$

Factor

$$\frac{61}{3 \cdot 5 \cdot 7} = 0.580952380952381$$