Solve -1/6*6/7+4/5*-1/3+frac{1}{3}*frac{1}{-1}

$$- \frac { 1 } { 6 } \cdot \frac { 6 } { 7 } + \frac { 4 } { 5 } \cdot - \frac { 1 } { 3 } + \frac { 1 } { 3 } \cdot \frac { 1 } { - 1 }$$

Evaluate

$$-\frac{26}{35}\approx -0.742857143$$

Solution Steps

Multiply -\frac{1}{6} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-6}{6\times 7}+\frac{4}{5}\left(-\frac{1}{3}\right)+\frac{1}{3}\times \frac{1}{-1}$$

Cancel out 6 in both numerator and denominator.

$$\frac{-1}{7}+\frac{4}{5}\left(-\frac{1}{3}\right)+\frac{1}{3}\times \frac{1}{-1}$$

Fraction \frac{-1}{7} can be rewritten as -\frac{1}{7} by extracting the negative sign.

$$-\frac{1}{7}+\frac{4}{5}\left(-\frac{1}{3}\right)+\frac{1}{3}\times \frac{1}{-1}$$

Multiply \frac{4}{5} times -\frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{7}+\frac{4\left(-1\right)}{5\times 3}+\frac{1}{3}\times \frac{1}{-1}$$

Do the multiplications in the fraction \frac{4\left(-1\right)}{5\times 3}.

$$-\frac{1}{7}+\frac{-4}{15}+\frac{1}{3}\times \frac{1}{-1}$$

Fraction \frac{-4}{15} can be rewritten as -\frac{4}{15} by extracting the negative sign.

$$-\frac{1}{7}-\frac{4}{15}+\frac{1}{3}\times \frac{1}{-1}$$

Least common multiple of 7 and 15 is 105. Convert -\frac{1}{7} and \frac{4}{15} to fractions with denominator 105.

$$-\frac{15}{105}-\frac{28}{105}+\frac{1}{3}\times \frac{1}{-1}$$

Since -\frac{15}{105} and \frac{28}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-15-28}{105}+\frac{1}{3}\times \frac{1}{-1}$$

Subtract 28 from -15 to get -43.

$$-\frac{43}{105}+\frac{1}{3}\times \frac{1}{-1}$$

Divide 1 by -1 to get -1.

$$-\frac{43}{105}+\frac{1}{3}\left(-1\right)$$

Multiply \frac{1}{3} and -1 to get -\frac{1}{3}.

$$-\frac{43}{105}-\frac{1}{3}$$

Least common multiple of 105 and 3 is 105. Convert -\frac{43}{105} and \frac{1}{3} to fractions with denominator 105.

$$-\frac{43}{105}-\frac{35}{105}$$

Since -\frac{43}{105} and \frac{35}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-43-35}{105}$$

Subtract 35 from -43 to get -78.

$$\frac{-78}{105}$$

Reduce the fraction \frac{-78}{105} to lowest terms by extracting and canceling out 3.

$$-\frac{26}{35}$$

Factor

$$-\frac{26}{35} = -0.7428571428571429$$