Solve 4/frac{1{4}-5/2}

$$\frac{ 4 }{ \frac{ 1 }{ 4 } - \frac{ 5 }{ 2 } }$$

Evaluate

$$-\frac{16}{9}\approx -1.777777778$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{1}{4} and \frac{5}{2} to fractions with denominator 4.

$$\frac{4}{\frac{1}{4}-\frac{10}{4}}$$

Since \frac{1}{4} and \frac{10}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{\frac{1-10}{4}}$$

Subtract 10 from 1 to get -9.

$$\frac{4}{-\frac{9}{4}}$$

Divide 4 by -\frac{9}{4} by multiplying 4 by the reciprocal of -\frac{9}{4}.

$$4\left(-\frac{4}{9}\right)$$

Express 4\left(-\frac{4}{9}\right) as a single fraction.

$$\frac{4\left(-4\right)}{9}$$

Multiply 4 and -4 to get -16.

$$\frac{-16}{9}$$

Fraction \frac{-16}{9} can be rewritten as -\frac{16}{9} by extracting the negative sign.

$$-\frac{16}{9}$$

Factor

$$-\frac{16}{9} = -1\frac{7}{9} = -1.7777777777777777$$