Solve (1/4-2/3)div1/4div(-3/5)

$$( \frac { 1 } { 4 } - \frac { 2 } { 3 } ) \div \frac { 1 } { 4 } \div ( - \frac { 3 } { 5 } )$$

Evaluate

$$\frac{25}{9}\approx 2.777777778$$

Solution Steps

Divide \frac{\frac{1}{4}-\frac{2}{3}}{\frac{1}{4}} by -\frac{3}{5} by multiplying \frac{\frac{1}{4}-\frac{2}{3}}{\frac{1}{4}} by the reciprocal of -\frac{3}{5}.

$$\frac{\left(\frac{1}{4}-\frac{2}{3}\right)\times 5}{\frac{1}{4}\left(-3\right)}$$

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{\left(\frac{3}{12}-\frac{8}{12}\right)\times 5}{\frac{1}{4}\left(-3\right)}$$

Since \frac{3}{12} and \frac{8}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3-8}{12}\times 5}{\frac{1}{4}\left(-3\right)}$$

Subtract 8 from 3 to get -5.

$$\frac{-\frac{5}{12}\times 5}{\frac{1}{4}\left(-3\right)}$$

Express -\frac{5}{12}\times 5 as a single fraction.

$$\frac{\frac{-5\times 5}{12}}{\frac{1}{4}\left(-3\right)}$$

Multiply -5 and 5 to get -25.

$$\frac{\frac{-25}{12}}{\frac{1}{4}\left(-3\right)}$$

Fraction \frac{-25}{12} can be rewritten as -\frac{25}{12} by extracting the negative sign.

$$\frac{-\frac{25}{12}}{\frac{1}{4}\left(-3\right)}$$

Multiply \frac{1}{4} and -3 to get \frac{-3}{4}.

$$\frac{-\frac{25}{12}}{\frac{-3}{4}}$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\frac{-\frac{25}{12}}{-\frac{3}{4}}$$

Divide -\frac{25}{12} by -\frac{3}{4} by multiplying -\frac{25}{12} by the reciprocal of -\frac{3}{4}.

$$-\frac{25}{12}\left(-\frac{4}{3}\right)$$

Multiply -\frac{25}{12} times -\frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-25\left(-4\right)}{12\times 3}$$

Do the multiplications in the fraction \frac{-25\left(-4\right)}{12\times 3}.

$$\frac{100}{36}$$

Reduce the fraction \frac{100}{36} to lowest terms by extracting and canceling out 4.

$$\frac{25}{9}$$

Factor

$$\frac{5 ^ {2}}{3 ^ {2}} = 2\frac{7}{9} = 2.7777777777777777$$