Solve (-1/9)(-4/7)+6/7/frac{1{10}-frac{6}{7}}

$$\frac{ (- \frac{ 1 }{ 9 } )(- \frac{ 4 }{ 7 } )+ \frac{ 6 }{ 7 } }{ \frac{ 1 }{ 10 } - \frac{ 6 }{ 7 } }$$

Evaluate

$$-\frac{580}{477}\approx -1.215932914$$

Solution Steps

Multiply -\frac{1}{9} times -\frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-\left(-4\right)}{9\times 7}+\frac{6}{7}}{\frac{1}{10}-\frac{6}{7}}$$

Do the multiplications in the fraction \frac{-\left(-4\right)}{9\times 7}.

$$\frac{\frac{4}{63}+\frac{6}{7}}{\frac{1}{10}-\frac{6}{7}}$$

Least common multiple of 63 and 7 is 63. Convert \frac{4}{63} and \frac{6}{7} to fractions with denominator 63.

$$\frac{\frac{4}{63}+\frac{54}{63}}{\frac{1}{10}-\frac{6}{7}}$$

Since \frac{4}{63} and \frac{54}{63} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+54}{63}}{\frac{1}{10}-\frac{6}{7}}$$

Add 4 and 54 to get 58.

$$\frac{\frac{58}{63}}{\frac{1}{10}-\frac{6}{7}}$$

Least common multiple of 10 and 7 is 70. Convert \frac{1}{10} and \frac{6}{7} to fractions with denominator 70.

$$\frac{\frac{58}{63}}{\frac{7}{70}-\frac{60}{70}}$$

Since \frac{7}{70} and \frac{60}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{58}{63}}{\frac{7-60}{70}}$$

Subtract 60 from 7 to get -53.

$$\frac{\frac{58}{63}}{-\frac{53}{70}}$$

Divide \frac{58}{63} by -\frac{53}{70} by multiplying \frac{58}{63} by the reciprocal of -\frac{53}{70}.

$$\frac{58}{63}\left(-\frac{70}{53}\right)$$

Multiply \frac{58}{63} times -\frac{70}{53} by multiplying numerator times numerator and denominator times denominator.

$$\frac{58\left(-70\right)}{63\times 53}$$

Do the multiplications in the fraction \frac{58\left(-70\right)}{63\times 53}.

$$\frac{-4060}{3339}$$

Reduce the fraction \frac{-4060}{3339} to lowest terms by extracting and canceling out 7.

$$-\frac{580}{477}$$

Factor

$$-\frac{580}{477} = -1\frac{103}{477} = -1.2159329140461217$$