Simplify (1 + 3/2) / 2 with Fractions

Problem

$\dfrac{1+\frac{3}{2}}{2}$

Step 1: Simplify inside the parentheses

Starting with the parentheses, $1+\frac{3}{2}$ must be combined before the outside division happens. Since $1$ is the same as $\frac{2}{2}$, we have

$$1+\frac{3}{2}=\frac{2}{2}+\frac{3}{2}=\frac{5}{2}.$$

Step 2: Apply the outside division

With the parentheses simplified to $\frac{5}{2}$, the expression becomes

$$\frac{5}{2}\div 2.$$

Dividing by $2$ is the same as multiplying by $\frac{1}{2}$, so

$$\frac{5}{2}\div 2=\frac{5}{2}\times \frac{1}{2}.$$

Step 3: Write the simplified fraction

Now multiply the numerators and denominators straight across:

$$\frac{5}{2}\times \frac{1}{2}=\frac{5\cdot 1}{2\cdot 2}=\frac{5}{4}.$$

So the simplified value is

$$\frac{5}{4}.$$