Basic Math Examples

$8 \frac{1}{2} \cdot (2) + 3 \frac{1}{4} \cdot (2)$

Step 1

Convert $8 \frac{1}{2}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$(8 + \frac{1}{2}) \cdot 2 + 3 \frac{1}{4} \cdot (2)$

Step 1.2

Add $8$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(8 \cdot \frac{2}{2} + \frac{1}{2}) \cdot 2 + 3 \frac{1}{4} \cdot (2)$

Step 1.2.2

Combine $8$ and $\frac{2}{2}$ .

$(\frac{8 \cdot 2}{2} + \frac{1}{2}) \cdot 2 + 3 \frac{1}{4} \cdot (2)$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 2 + 1}{2} \cdot 2 + 3 \frac{1}{4} \cdot (2)$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $8$ by $2$ .

$\frac{16 + 1}{2} \cdot 2 + 3 \frac{1}{4} \cdot (2)$

Step 1.2.4.2

Add $16$ and $1$ .

$\frac{17}{2} \cdot 2 + 3 \frac{1}{4} \cdot (2)$

Step 2

Convert $3 \frac{1}{4}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

$\frac{17}{2} \cdot 2 + (3 + \frac{1}{4}) \cdot 2$

Step 2.2

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

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Step 2.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{17}{2} \cdot 2 + (3 \cdot \frac{4}{4} + \frac{1}{4}) \cdot 2$

Step 2.2.2

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

$\frac{17}{2} \cdot 2 + (\frac{3 \cdot 4}{4} + \frac{1}{4}) \cdot 2$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{17}{2} \cdot 2 + \frac{3 \cdot 4 + 1}{4} \cdot 2$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $4$ .

$\frac{17}{2} \cdot 2 + \frac{12 + 1}{4} \cdot 2$

Step 2.2.4.2

Add $12$ and $1$ .

$\frac{17}{2} \cdot 2 + \frac{13}{4} \cdot 2$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Cancel the common factor.

$\frac{17}{2} \cdot 2 + \frac{13}{4} \cdot 2$

Step 3.1.2

Rewrite the expression.

$17 + \frac{13}{4} \cdot 2$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $4$ .

$17 + \frac{13}{2 (2)} \cdot 2$

Step 3.2.2

Cancel the common factor.

$17 + \frac{13}{2 \cdot 2} \cdot 2$

Step 3.2.3

Rewrite the expression.

$17 + \frac{13}{2}$

Step 4

To write $17$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$17 \cdot \frac{2}{2} + \frac{13}{2}$

Step 5

Combine $17$ and $\frac{2}{2}$ .

$\frac{17 \cdot 2}{2} + \frac{13}{2}$

Step 6

Combine the numerators over the common denominator.

$\frac{17 \cdot 2 + 13}{2}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $17$ by $2$ .

$\frac{34 + 13}{2}$

Step 7.2

Add $34$ and $13$ .

$\frac{47}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{47}{2}$

Decimal Form:

$23.5$

Mixed Number Form:

$23 \frac{1}{2}$