Question

Simplify the following expression:

Answer 1

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

To begin, we can simplify the expression's denominator by finding a common denominator between the denominators of the fractions in the denominator.  To make them compatible, we can convert $\frac{5}{2}$ into $\frac{10}{4}$:

$\frac{4}{ \frac{1}{4} - \frac{5}{2}( \frac{2}{2}) } = \frac{4}{ \frac{1}{4} - \frac{10}{4} }$

Next, we can simplify:

$\frac{4}{ \frac{1}{4} - \frac{10}{4} } = \frac{4}{ -\frac{9}{4}}$

Finally, to cancel the denominator within the denominator, we can multiply the whole expression by $\frac{4}{4}$, or 1:

$\frac{4}{ -\frac{9}{4}}* \frac{4}{4} = -\frac{16}{9}$

The expression simplifies to $-\frac{16}{9}$, or $-1 \frac{7}{9}$ as a mixed number.

Answer 2

The step by step simplification is shown below.

$\frac{4}{ \frac{1}{4}-\frac{5}{2}} \\ \\ = \frac{4}{ \frac{1-2(5)}{4} } \\ \\ = \frac{4}{ \frac{-9}{4} } \\ \\ =4* \frac{-4}{9} \\ \\ = - \frac{16}{9}$

Therefore the answer is -16/9