Evaluate 4/(3/4-3/2)

$\frac{4}{\frac{3}{4} - \frac{3}{2}}$

Step 1

Simplify the denominator.

To write $- \frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4}{\frac{3}{4} - \frac{3}{2} \cdot \frac{2}{2}}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{2}$ by $\frac{2}{2}$ .

$\frac{4}{\frac{3}{4} - \frac{3 \cdot 2}{2 \cdot 2}}$

Multiply $2$ by $2$ .

$\frac{4}{\frac{3}{4} - \frac{3 \cdot 2}{4}}$

Combine the numerators over the common denominator.

$\frac{4}{\frac{3 - 3 \cdot 2}{4}}$

Simplify the numerator.

Multiply $- 3$ by $2$ .

$\frac{4}{\frac{3 - 6}{4}}$

Subtract $6$ from $3$ .

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

Move the negative in front of the fraction.

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

Step 2

Multiply the numerator by the reciprocal of the denominator.

$4 (- \frac{4}{3})$

Step 3

Multiply $4 (- \frac{4}{3})$ .

Multiply $- 1$ by $4$ .

$- 4 (\frac{4}{3})$

Combine $- 4$ and $\frac{4}{3}$ .

$\frac{- 4 \cdot 4}{3}$

Multiply $- 4$ by $4$ .

$\frac{- 16}{3}$

Step 4

Move the negative in front of the fraction.

$- \frac{16}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{16}{3}$

Decimal Form:

$- 5.\overline{3}$

Mixed Number Form:

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