Solve 1+1/3*3/5/frac{1{3}-3/5}

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

Evaluate

$$-\frac{9}{2}=-4.5$$

Solution Steps

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

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

Cancel out 3 in both numerator and denominator.

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

Convert 1 to fraction \frac{5}{5}.

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

Since \frac{5}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

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

Add 5 and 1 to get 6.

$$\frac{\frac{6}{5}}{\frac{1}{3}-\frac{3}{5}}$$

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

$$\frac{\frac{6}{5}}{\frac{5}{15}-\frac{9}{15}}$$

Since \frac{5}{15} and \frac{9}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6}{5}}{\frac{5-9}{15}}$$

Subtract 9 from 5 to get -4.

$$\frac{\frac{6}{5}}{-\frac{4}{15}}$$

Divide \frac{6}{5} by -\frac{4}{15} by multiplying \frac{6}{5} by the reciprocal of -\frac{4}{15}.

$$\frac{6}{5}\left(-\frac{15}{4}\right)$$

Multiply \frac{6}{5} times -\frac{15}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6\left(-15\right)}{5\times 4}$$

Do the multiplications in the fraction \frac{6\left(-15\right)}{5\times 4}.

$$\frac{-90}{20}$$

Reduce the fraction \frac{-90}{20} to lowest terms by extracting and canceling out 10.

$$-\frac{9}{2}$$

Factor

$$-\frac{9}{2} = -4\frac{1}{2} = -4.5$$