Basic Math Examples

$\frac{1}{2} \cdot (3) + \frac{1}{4} \cdot (3) + 40$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{2}$ and $3$ .

$\frac{3}{2} + \frac{1}{4} \cdot (3) + 40$

Step 1.2

Combine $\frac{1}{4}$ and $3$ .

$\frac{3}{2} + \frac{3}{4} + 40$

Step 2

Find the common denominator.

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Step 2.1

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

$\frac{3}{2} \cdot \frac{2}{2} + \frac{3}{4} + 40$

Step 2.2

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

$\frac{3 \cdot 2}{2 \cdot 2} + \frac{3}{4} + 40$

Step 2.3

Write $40$ as a fraction with denominator $1$ .

$\frac{3 \cdot 2}{2 \cdot 2} + \frac{3}{4} + \frac{40}{1}$

Step 2.4

Multiply $\frac{40}{1}$ by $\frac{4}{4}$ .

$\frac{3 \cdot 2}{2 \cdot 2} + \frac{3}{4} + \frac{40}{1} \cdot \frac{4}{4}$

Step 2.5

Multiply $\frac{40}{1}$ by $\frac{4}{4}$ .

$\frac{3 \cdot 2}{2 \cdot 2} + \frac{3}{4} + \frac{40 \cdot 4}{4}$

Step 2.6

Multiply $2$ by $2$ .

$\frac{3 \cdot 2}{4} + \frac{3}{4} + \frac{40 \cdot 4}{4}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 \cdot 2 + 3 + 40 \cdot 4}{4}$

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $2$ .

$\frac{6 + 3 + 40 \cdot 4}{4}$

Step 4.2

Multiply $40$ by $4$ .

$\frac{6 + 3 + 160}{4}$

Step 5

Simplify by adding numbers.

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Step 5.1

Add $6$ and $3$ .

$\frac{9 + 160}{4}$

Step 5.2

Add $9$ and $160$ .

$\frac{169}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{169}{4}$

Decimal Form:

$42.25$

Mixed Number Form:

$42 \frac{1}{4}$