Solve -1/3-(-7/5)/1+(-frac{7{5})(-1/3)}

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

Evaluate

$$\frac{8}{11}\approx 0.727272727$$

Solution Steps

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

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

The opposite of -\frac{7}{5} is \frac{7}{5}.

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

Least common multiple of 3 and 5 is 15. Convert -\frac{1}{3} and \frac{7}{5} to fractions with denominator 15.

$$\frac{-\frac{5}{15}+\frac{21}{15}}{1-\frac{7}{5}\left(-\frac{1}{3}\right)}$$

Since -\frac{5}{15} and \frac{21}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-5+21}{15}}{1-\frac{7}{5}\left(-\frac{1}{3}\right)}$$

Add -5 and 21 to get 16.

$$\frac{\frac{16}{15}}{1-\frac{7}{5}\left(-\frac{1}{3}\right)}$$

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

$$\frac{\frac{16}{15}}{1+\frac{-7\left(-1\right)}{5\times 3}}$$

Do the multiplications in the fraction \frac{-7\left(-1\right)}{5\times 3}.

$$\frac{\frac{16}{15}}{1+\frac{7}{15}}$$

Convert 1 to fraction \frac{15}{15}.

$$\frac{\frac{16}{15}}{\frac{15}{15}+\frac{7}{15}}$$

Since \frac{15}{15} and \frac{7}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{16}{15}}{\frac{15+7}{15}}$$

Add 15 and 7 to get 22.

$$\frac{\frac{16}{15}}{\frac{22}{15}}$$

Divide \frac{16}{15} by \frac{22}{15} by multiplying \frac{16}{15} by the reciprocal of \frac{22}{15}.

$$\frac{16}{15}\times \frac{15}{22}$$

Multiply \frac{16}{15} times \frac{15}{22} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\times 15}{15\times 22}$$

Cancel out 15 in both numerator and denominator.

$$\frac{16}{22}$$

Reduce the fraction \frac{16}{22} to lowest terms by extracting and canceling out 2.

$$\frac{8}{11}$$

Factor

$$\frac{2 ^ {3}}{11} = 0.7272727272727273$$