Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.2

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

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Step 1.2.1

Combine $\frac{3}{2}$ and $3$ .

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

Step 1.2.2

Multiply $3$ by $3$ .

$\frac{9}{2} + \frac{1}{2} \cdot \frac{3}{2}$

Step 1.3

Multiply $\frac{1}{2} \cdot \frac{3}{2}$ .

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Step 1.3.1

Multiply $\frac{1}{2}$ by $\frac{3}{2}$ .

$\frac{9}{2} + \frac{3}{2 \cdot 2}$

Step 1.3.2

Multiply $2$ by $2$ .

$\frac{9}{2} + \frac{3}{4}$

Step 2

To write $\frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9}{2} \cdot \frac{2}{2} + \frac{3}{4}$

Step 3

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

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Step 3.1

Multiply $\frac{9}{2}$ by $\frac{2}{2}$ .

$\frac{9 \cdot 2}{2 \cdot 2} + \frac{3}{4}$

Step 3.2

Multiply $2$ by $2$ .

$\frac{9 \cdot 2}{4} + \frac{3}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{9 \cdot 2 + 3}{4}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $9$ by $2$ .

$\frac{18 + 3}{4}$

Step 5.2

Add $18$ and $3$ .

$\frac{21}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{21}{4}$

Decimal Form:

$5.25$

Mixed Number Form:

$5 \frac{1}{4}$